# find the derivative of the function f(x)= tan (10x^2)

94,588 results

### calculus

find the derivative of the function f(x)= tan (10x^2)

### Derivatives- Math

Can someone explain how to find the derivative of : 1. y= 5^ãx / x And the second derivative of: y= xe^10x For this question I got up to the first derivative and got this y = e^10x + 10xe^10x but I can't seem to get the correct answer for the second derivative.

### calculus

1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the graph of f(x) = -2x3...

### calculus

5. Find the equation of the tangent line to the graph of f(a) = -sec(a) at the point (0, -1) 6. Differentiate y = sin(x)tan(x). 7. Find f '(x) for f(x) = sin(x)cot(x). 8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex.

### Calculus

Find the derivative of the following function: f(x)= 10x-3/5x +6x

### math

Find the derivative of the function f by using the rules of differentiation. f(x)=(9x^3+3x^2+10x-6)/(x)

### Calc

intergral of (x^3 -4x + 3)/(2x) dx would this be ln abs(x^3-4x+3) + C? I don't really understand how to solve this problem. d/dx (tan (x^2)) sec^2(x^2)(2x) would this be the correct answer to find the derivative of tan (x^2)? no, because if you differentiate your answer you ...

### calculus

8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex. 10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x) 11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has a slope of 0. 12. If the slope of a ...

### Calculus

1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). 4. Find the derivative of 2^(e^(sin x)). ...

### calculus

Please find the Derivative of the function y =sec^2x + tan^2x

### Calculus Help

Use logarithmic differentiation to find the derivative of the function. y = (tan x)^(7/x)

### Calc

a) y =ln(x-1) find dy/dx=? b) y=3 ln x - ln (1/x) where x >0, dy/dx= ? My teacher says the answers are a) (2x)/(x^2-1) and b) 4/x I am not sure how you find the derivative when they involve ln. Could you please explain to me how to get these answers? I have a quiz on them ...

### Maths Calculus Derivatives

Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x) - tan^2(100x)} / x

### Algebra HELP!

Consider the function h as defined. Find functions f and g so (f o g)(x)=h(x) h(x)=8/x^2+10 I think it is: h(x)=8/x^2+10 h(x)=8/x^2+10*x^2/x^2 h(x)=8/x^2+10x^2/x^2 h(x)=8+10x^2/x^2 h(x)=10x^2+8/x^2 h(x)=2(5x^2)+2(4)/x^2 h(x)=2(5x^2+4)/x^2

### Calculus

Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of the inverse function evaluated in 9] . I don...

### calculus

You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the derivative of the function using the definition of derivative. (b) Give the domain of the function. c) Give the domain of derivative of function?

### calculus

Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)

### calculus

find dy/dx y=ln (secx + tanx) Let u= secx + tan x dy/dx= 1/u * du/dx now, put the derivative of d secx/dx + dtanx/dx in. You may have some challenging algebra to simplify it. Use the chain rule. Let y(u) = ln u u(x) = sec x + tan x dy/dx = dy/du*du/dx dy/du = 1/u = 1/(sec x + ...

### Calculus

Use a symbolic differentiation utility to find the derivative of the function g(x)=xã((x^2)+1). Use the utility to graph the function and is derivative on the same set of coordinate axes. Describe the behavior of the function that corresponds to any zeroes of the graph of ...

### Calc

g'(x)=tan(2/1+x^2) Let g be the function with first derivative given above and g(1)=5. If f is the function defined by f(x)=ln(g(x)), what is the value of f'(1)? I know the answer is 0.311, but I need steps as to why. Please and thanks.

### Calculus

find the derivative: d/dx int_a to x (a being the upper limit) of tan(tan(t))dt

### Calculus

Differentiate to find critical numbers and leave function in fully factored form. g(x) = (x^2+1)^5(x^2+2)^6 g'(x) = (x^2+1)^5[6(x^2+2)^5(2x)] + (x^2+2)^6[5(x^2+1)^4(2x)] g'(x) = 2x(x^2+1)^4(x^2+2)^5[6(x^2+2)(2x) + 5(x^2+1)(2x)] g'(x) = 2x(x^2+1)^4(x^2+2)^5(11x^2+11) g'(x) = ...

### Calc (Derivatives)

I understand finding the derivative and there is a simpler way of doing so, however, can someone show you derive at these answers by the DEF'N of Derivatives? Much appreciated! Question 1: Find, from the definition, the derivative, f'(x), for f(x)=5x^2-3x+1 . Answer: f ’(x...

### Math

Find the equation of the tangent line 5x^2+y^2=14 at (1,3). P.S: It's calculus. So far I know this much 10x+2y(dy/dx)=o -10x -10x ___________________ 2y(dy/dx)= -10x (dy/dx)= -10x/2y= -5x/y m= -5(1)/3= -5/3 y=mx+b 3= -5/3(1)+b then what?

### Derivative

Can you help me find the derivative of y= cos(x)/1+sin(x).. the / is a fraction bar. I have a hard time finding trig derivatives because I don't really know what the derivative of cos,sin ,or tan would be honestly.

### calculus

Find the derivative of the function 1)f(t)=tan(e^2t)+e^tan2t f'(t)= [im not quite sure with this. im assuming the implicit differentiation] 2) F(t)=e^(8tsin2t) [for this one i got 2e^(8t)(4sin(2t)+cos(2t)) but it is incorrect.

### Calculus 1A

I am trying to find: dy/dx for y = sec(tan x) I have the answer, but I have no idea how to get there. I know that the derivative of sec x = sec x tan x and that the derivative of tan x is sec^2 x. But sec doesn't have an x, so ...?

### Calculus

Find the intervals on which y=1/(x^2+1)^2 is increasing and decreasing. find the first derivative which is -4x/(x^2+1)^3 you should know that if the first derivative is positive, then the function is increasing and if it is negative, the function is decreasing. Now by ...

### CAL- derivative

Find the derivative; y= x^3(5x-1)^4 So this is my answer y'=2x(5x-1)^3 + 10x + x(5x-1) Please correct me if my answer is wrong.

### Math - derivative of sinusoidal (check)

a) Find a function y=f(x) that satisfies the differential equation dy/dx = fifth derivative. This is one of the questions in my practice test, I tried the basic equation of the trig function such as f(x)= sin(x) or f(x)=-sin(x) however in the fourth derivative they reach the ...

### calculus

(i know i've asked so many questions. i just want to make sure my answers are right for this homework! hopefully it isn't too annoying for you :) ) Find the derivative of the given function. y=(tan^-1)√(3x) A. (1)/(√(1-3x)) B. (1)/(6√(3x(1+3x))) C. (3)/(2(1+...

### Trigonometry

Find the exact value of tan(a-b) sin a = 4/5, -3pi/2<a<-pi; tan b = -sqrt2, pi/2<b<pi identity used is: tan(a-b)=(tan a-tan b)/1+tan a tan b simplify answer using radicals. (a is alpha, b is beta)

### Calculus : Derivative

If tan^-1(x^2-y^2/x^2+y^2) = a, prove that dy/dx = x(1 - tan a)/y(1 + tan a) Please solve!!!

### CALC 1

Suppose that h is a function with h'(x) = xe^x. Find all intervals where the function h is concave up. Now, I understand that concavity is determined by the second derivative, so what my question here is, is it just taking the first derivative and then taking it again? Is it ...

### Pre-Cal

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. (tan(74°)-tan(14°))/(1+tan(74°)tan(14°)) =__________ Find it's exact value (not decimal form) =__________ Note: A similar question(but with different degrees) had the ...

### calculus

please help! having issue with exponent part of problem. I come to 16x^4 but I think it should be 16x^3.i also have complications with finding the domains. find the derivative of the function using the definition of derivative. f(x)=4x^4 f'(x)=? State the domain of the ...

### Derivative Calculus

I just need my answers checked. 1) Find the derivative. f(x)=3x^5/4 - 8/9x^9/8 + x^2 - 9x + 1 Answer: f’(x)= 15/4x^1/4 - x ^1/8 + 2x -9 2) Let f(x)= 7x^3 - 9x. Find f’(5) Answer: f’(x)=21x^2-9 f’(5)=516 3) Find the given limit by evaluating the derivative. lim h⇒...

### increasing decreasing and more

How to analytically find the intervals on which the function y = 2x^4 - 4x^2 + 1 is 1)increasing 2)decreasing 3)concave up 4)concave down Also find any local extreme values and inflection points. Thanks. (1) The function is increasing when the first derivative dy/dx = 8x^3 - ...

### Calculus

For f(x)=2(x+5)^3 +7 Find and classify the extreme values, determine where the function is increasing and decreasing, where it is concave up and concave down, and any points of inflection. I understand this is using the first and second derivative tests, but I can't find any ...

### CAL

The _____________ of a function is a formula for the slope of the tangent line to that function at any point x. When the function is defined as f(x), the derivative will be written as __________or ________. When the function is written in the form of y =, the derivative is ...

### increasing and decreasing intervals

Have to find the intervals on which f(x) = 4 - sqrt(x+2) is increasing. Also the intervals on which the function is decreasing. TIA Find the derivative of f(x). When the derivative is positive, the function increases as x increases. When the derivative is negative, the ...

### math

Let f be a real value function and x Î Df then 0 lim ( ) ( ) h f x h f x ® h + - when it exists is called A) The derivative of f at a B) The derivative of f at h C) The derivative of f at x D) The derivative of f at x = h

### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative Please show me how u got this!!

### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection points Please show me how u got this!

### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any inflection points Please show me how u got this!

### Calculus

I'm having a little trouble with this problem...it would be great if you could point out where I'm going wrong. Hours of Daylight as a Function of Latitude. Let S(x) be the number of sunlight hours on a cloudless June 21st, as a function of latitude, x, measured in degrees. a...

### math

I have the same project as Jill down there... -What is the definition of a derivative? -What does the derivative of a function tell you (in english) ? Then I need an example of the power rule, quotient rule, and chain rule. -What information does the FIRST derivative tell you ...

### Quantum mechanics, eigenfunctions!

Determine if the function sin(x)*e^(ax) where a=constant is an eigenfunction of the operators d/dx and d^2/(dx)^2 Okay. My understanding is that you use the operator and perform its "thing" on the function. In this case, you will have to find the 1st derivative of sin(x)*e^(ax...

### Calculus. Please help!

Find the minimum value of the function f(x,y= 25x^2+3y^2+20xy+10x+4y+10 subject to the constraint 5x^2+4xy=1. I solved fx=50x+20y+10 fy=6y+20x+4 gx=10x+4y gy=4x Then what?

### Math

find the derivative of x^3-6x^2+15x+8 and show by completing the square that function has no turning point. I can find derivative but not sure of next step

### CAL

Hi, im lost in theses three problems. Please help. Thank you so much!!! 1. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = 3 squareroot all 1 + 5x (g(x), f(u)) = ??????? Find the derivative dy/dx. 2...

### calc

Consider the function below. (Round the answers to two decimal places. f(x) = 2x tan(x) -p/2 < x < p/2 (a) Find the interval where the function is increasing. Find the interval where the function is decreasing. (b) Find the local minimum value. (c) Find the interval ...

### Math

Consider the function f(x) whose second derivative is f(x)=10x+2sin(x). If f(0)=4 and f'(0)=4, what is f(x)? Please do not include the constant (+C) in your answer. I got f(x) to be (10/6)x^3-2sin(x), but don't really know what to do with the f(0)=4

### calculus pleas pleas help, derivates

what is the derivative of x/tan(x) and find f'(pi/4) f'(x)=(tanx-x*sec(x)^2)/(tanx)^2 That's the quotient rule for derivatives or as my teacher says: Low,low, low D'High, minus High d'low all over low square that's the quotient rule. It's a song which helps. D'High or d'low ...

### Calculus derivatives

f(a) = a + √a (a) Find the derivative of the function using the definition of derivative.

### calculus

Calculate the derivative of the function. Then find the value of the derivative as specified. f(x) = 8/(x+2); f '(0)

### Calculus

Find the derivative of 10x^2+4y^2=sqrt(7). Is the answer 20x+8y=0

### Calculus

Use derivative formulas to find the derivative of the function. please show your work h(x)=10^3-25x^6+3x^15

### partial differentiation

u(x,y)=xln(x^2+y^2)-(2y times inverse of tan of y/x) 1)find derivative of u wrt to x and then wrt y 2)show that (x times derivative of u wrt x)+(y times derivative of u wrt y) = u +2x

### Derivative

if g(x)= 5x^6-3/x^2, find the 3rd and 5th derivative of the function. Pls help!

### Calculus-Function

sketch the graph of a function in neighborhood x=2 that satisfies these conditions f(2)=3 f'(2)=2 f"(2)=-1 you can find a specific function that satisfies all of the given conditions i know the first derivative gives you critical points, and second derivative gives you points ...

### Calculus

Find the derivative of the function using the definition of a derivative. F(x)=squareroot(1-3x) Please show work for understanding, thank you! :)

### Applied Calculus

Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first derivative to be 10/(7x+10)^2

### CALCULUS HELP

Find the second derivative for the function 5x^3+60x^2-36x-41 and solve the equation F(X)=0 i got to the second derivative but what do we do next to be able to get one of these answers.. F(x) = 5x3+60x2−36x−41 1. derivative of F(x) with respect to x = 15x2+120x&#...

### Math - derivative of a rational function

find the 1st derivative of f(x) = x/(x-1)2 Is the 1st derivative f'(x)= -x-1/(x-1)^3

### maths

Derivative of √ tan x is, Answer: A. sin 2 x/ √ tan x B. cos 2 x/ 2 √ tan x C. sec 2 x D. None of these

### trig help much appreciated! :))

1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove that tan2 – 1 + cos2 = tan2 sin2 . 5. ...

### math

f(x)= 5x^2+8x+7/x^1/2 i have to find the derivative and when I do this is what i get.... (x^.5)(10x+8)-(5x^2+8x+7)(-.5x^-3/2)/(x) it says that i am wrong however please help

### Calculus review

let the function h(x)= (integrand symbol from 2 to x^2)arctan (t) dt. Find h'(x). This question confused me because i know the derivative of an integral is the original function. I just need help with finding the derivative of that integral. I don't know how to post integral ...

### Calculus

What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? How would taking the derivative of the function in its original form look different when using log ...

### Calc.

What function would have a derivative of ƒ′(x) = 12x2 + 4x − 10? Explain how you arrived at your answer...I believe the answer is this: f(x)=4x^3+2x^2-10x...and I got this using the power rule and multiplying. Thanks.

### calculus

find the derivative for y= (tan^-1)e^x

### Calculus

How do you find the derivative of y=tan^2(x^4)?

### Math

find the derivative F(x)=tan(ln(5x))

### Math help!

Find the derivative of tan(ln(5x))

### Calculus - derivatives

Okay, I want to find the derivative of (x^x)^(x^x)... Well, I already went through the process of finding the derivative of just x^x (I used ln to do this). This is what I found... dy/dx = x^x(lnx+1) So now I want to find the derivative of (x^x)^(x^x) (using ln). This is what ...

### Calc

If f(x)= sec x, find f"(Pi/4) I am not sure how to take the 2nd derivative? f'(x)= sec x tan x f"(x)=??? Is it f"(x)= (sec x tan x)(sec^2x)??? Please Help!

### math

Hi, I am in need of some help. How would I find the derivative of the function: f(x) = int e^sin(t) dt if the upper bound is x^2 and the lower bound is cos(x)? I'm not really sure what to do here since e^sin(t) is not an integratable function. Should I instead integrate the ...

### inverse

If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means f inverse of 1 doesn't exist. I didn't ...

### calculus

please help! Find the derivative of f when f(x) = 5 tan^-1 (e^-x) + 6e^x

### Calculus

How do i find the second derivative of f(x)= tan(1-x)^1/2

### Calculus derivative

find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the derivative equation?

### Math

Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value. (tan(π/2)+tan((2π)/3)) / (1-tan(π/2)tan((2π)/3)) Answer=__________ Exact value answer=_________ ~Thank you.. I thought ...

### more trig.... how fun!!!!

if you can't help me with my first question hopw you can help me with this one. sec(-x)/csc(-x)=tan(x) thanx to anyone who can help From the definition of the sec and csc functions, and the tan function, sec(-x)/csc(-x) = sin(-x)/cos(-x) = tan(-x) However, tan (x) does not ...

### Math - Derivative of a polynomial function(check)

The red squirrel population, p, in a neighborhood park can be modelled by the function p(t)= srqt(210t+44t^2), where t is time in year. a) Determine the rate of growth of the squirrel population at t= 2years Ans: find the 1st derivative and substitute 2 in the function. b) ...

### Math (Calculus)

Find the derivative of (ln(tan(x))/3pi

### Math PLEASE PLEASE HELP ME

1.Find the derivative of the function. f(t) = (1+squrt t)(8t^2-7) 2. Find the derivative of the function. f(x) = (x^3 - 4)/(x^2 + 4)

### MATH

We now have d dx [x5 + y8] = 5x4 + 8y7y' = d dx [9] = 0. Rearranging this, we get 8y7y' = ?????????? ------------------------------------- A table of values for f, g, f ', and g' is given. x f(x) g(x) f '(x) g'(x) 1 3 2 4 6 2 1 8 5 7 3 7 2 7 9 (a) If h(x) = f(g(x)), find h'(3...

### Math22

1. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y= (g(x), f(u)) = 2. Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] y = ...

### Calc

I'm creating a "calculu for dummies" project book. I've already done most of it, I'm just stuck on these ones. Thank you! -What is the definition of a derivative? -What does the derivative of a function tell you (in english) ? Then I need an example of the power rule, quotient...

### math

f(x) = x^2 + 10x + 24 =(x^2 + 10x)+ 24 =(x^2 + 10x + 25 - 25) + 24 f(x) =(x+5)^2 - 1 Vertex: (-5, -1) How do you sketch this? I know that in the graph one of the coord is (-5, -1) but how do I find the others in order to make a parabola? :|

### calculus

i have to find the derivative (first) of y= tan^2 (3x-π) ^that is (3x- pi)

### Calculus

Find the derivative of y = ln |cos(ln)|. I got -tan(ln x)/x, is this correct?

### Calculus c

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a horizontal tangent at ...

### Maths

Given the quadratic function y =3x^2+10x-8 (i)Find the y-intercept. (ii)Find the x-intercept. (iii) Calculate the axis of symmetry. (iv)Find the coordinates of the vertex (v)Sketch the graph of the above function.

### Calculus-verify

What is the second derivative of f(x) = 5/3x^(3) - x^(3/2) + 6? Second derivative of f(x) = 5/3x^(3) - x^(3/2) + 6 is f''(x)=10x + 3/(4sqrt of x)

### calc

derivative of (x^3/6)+(1/2x)? i got (x^2/2)-(1/2x^2) is that correct? and then wut is the (F'(x))2?...meaning the derivative squred? if you meant (1/2)x^2 - 1/(2x^2) you are correct I don't think they are looking for the square of the derivative, but rather the second ...

### Calculus

Consider a differentiable function f having domain all positive real numbers, and for which it is known that f'(x)=(4-x)x^-3 for x>0. A. Find the x-coordinate of the critical point of f. Determine whether the point is a relative maximum, a relative minimum, or neither for ...

### PreCalc

Consider the function(7+15x^2)/(10x^2+9x+10). Find the function's domain and identify any horizontal and vertical asymptotes Please Help!