# Calculus (Derivatives of Inverse Functions)

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Calculus (Derivatives of Inverse Functions)
Suppose f(x) = sin(pi cos(x)). On any interval where the inverse function y = f^-1(x) exists, the derivative of f^-1(x) with respect to x is: I've come as far as y = arccos ((arcsin(x))/pi), but I am not certain this is right.

Pre Calculus
Inverse functions what is the inverse function of f(x)=1/square root of x +1? and f(x)=1-x^2, x<0?

calculus - derivatives
can you please find the first 5 derivatives for: f(x) = (0.5e^x)-(0.5e^-x) f'(x) = ? f''(x) = ? f'''(x) = ? f''''(x) = ? f'''''(x) = ? thanks :) f(x) = (0.5e^x)-(0.5e^-x) f'(x) = 0.5 e^x + 0.5 e^-x f''(x) = 0.5 e^x - 0.5 e^-x f'''(x) = 0.5 e^x + 0.5 e^-x f''''(x) = 0.5 e^x - 0...

Calculus
F(x) = 1-x and g(x) = 1/x These functions have the property that f = f^-1(inverse) and g = g ^-1. That is, the inverse of f is equal to itself and the inverse of g is also equal to itself. Take the composition of each function with itself to show that this is true. Remember, ...

calculus
Find the derivatives of the functions k(x)=(x^3+e^x)^4

Math - Inverse Functions
Find the inverses of the following functions. y = 3(x - 1)^2, x >= 1 Work: x = 3(y - 1)^2 x = 3(y - 1)(y - 1) x = 3(y^2 - y - y + 1) x = 3y^2 - 6y + 3 And now what do I do!? Please explain and show me how to solve this inverse function! ... Thank you

Calculus-Inverse Functions
is the inverse function of x+ floor(x) equal to x - floor (x/2) i got this after plotting points but i'm not sure. thank you

What is the inverse of each of the functions defined by the following equations, if the inverse exists. If the inverse does not exist for the largest possible domain, limit the domain so that the inverse will exist. In each case, give the domain and range of both the function ...

Calculus
Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would be considered the outside and inside.

Calculus: Derivatives
I'm having trouble understanding what derivatives in calculus (instantaneous speed) is. Can someone please explain it to me, or provide some easy links to learn from? Thanks!

Calculus
Hello, I really need help on these two homework problem. >< In problem #1, I believe it is related to the exponential functions and their derivatives section...in Calculus II? So, surely there should be a ln in the solution as well? I would like a step by step process ...

graph!
how can the graph of f(x)= X^2-4X be used to obtain the graph of y=g(x) ?????? don't know can you help me out? What is g(x)? The inverse function of f(x)? http://www.uncwil.edu/courses/mat111hb/functions/inverse/inverse.html

Calculus
[Inverse Functions] f(x)= 5cos(x)sin^(-1)(x) f'(x)=?

Pre-Calculus
Find the inverse function for the function f(x)=2^(x)+1/2^(x)-1 You will need to use some properties of logarithmic functions to find the inverse of this particular function.

Math
If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function? Explain your reasoning.

A student writes, "The inverse of y = -√(x+2) is y = x^2 - 2." Why is this statement false? I don't understand how it isnt the inverse. The textbook says that changing the domain will make it the inverse? Wouldn't that only make it a function?

Calculus III
Derivative of Inverse Trigonometric Functions f(x) = sin(arccos(4x)) What is f'(x)?

Calculus III
Derivative of Inverse Trigonometric Functions f(x) = cos(arcsin(2x)) What is f'(x)?

Calculus
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2 the sqrt is just over t.

Calculus

CALCULUS
show that f(x) = x^2-1 (x is greater than and equal to 0) and g(x) = root(x-1) (x is greater than and equal to -1) are inverse functions. when i try f(g(x)) = x and g(f(x)) = x to show that the two functions are inverses it doesn't work because i am not left with x when i ...

Linear Algebra
which of the following functions is the inverse of F(X)=3x F(X)=-3X F(X)=X (cubed)**** F(X)= X/3 This function does not have an inverse. Thank you!

Calculus Can you help
Suppose the functions f and g and their derivatives have the following values at x = 1 and x = 2. Let h(x) = f(g(x)). Evaluate h′(1). X | f(x) G(x) f'(x) g'(x) ____________________________ 1 | 8 2 1/3 -3 2 | 3 -4 2π 5 My answer: -6π but I'm not really sure if I...

Calculus
Find the derivatives, dy/dx for the following functions. a. x^2y^4 = lnx + 3y b. y = ln(2x^2 + 1) c. y = ln(ãx) d. y = lnx/x e. y = x^2 lnx f. y ß log_2⁡(3x)

Calculus
Integrate [1/square root of(e^(2x)-1)]. I have to use u substitution. We are doing the integrals of inverse trig functions, but I cannot get it to work out!

Find the inverse of the function y = (square root x) + 4x , then solve for its 1st order derivative.

Algebra
Use composition of functions to show that the functions f(x) = 5x + 7 and g(x)= 1/5x-7/5 are inverse functions. That is, carefully show that (fog)(x)= x and (gof)(x)= x.

Inverse functions
Solve for y to determine the inverse y=2-(1/2x)

Inverse Functions
Given that g is the inverse function of f, and f(3)=4, and f'(3)=5, then g'(4)= ?

calculus
find the second-order partial derivatives of f(x,y)=x^3 + x^2y^2 + y^3 + x+y and show that the mixed partial derivatives fxy and fyx are equal

Math - Calculus 1
Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2

Pre Calculus
Inverse functions find the value If f(x)=1/x, find f^-1 (2)

End behavior models
Thanks for the help with my previous problems Roger & Leo. It was really helpful. Now I want to know how to find the right and left end behavior models and horizontal tangents for the inverse functions, say y = tan inverse(x) I have to do this for all functions, but at least ...

((I forgot how to do find inverse functions and this is important)) Find the inverse function of g(x) = 2x + 4. A) g^(-1)(x) = 4x + 2 B) g^(-1)(x) = 2x + 1/2 C) g^(-1)(x) = 1/2x - 2 D) g^(-1)(x) = 2x - 4 I *think* it might be C but I'm not sure.

inverse functions
1-3cos=sin squared You need to define the variables, such as x, y etc. If you are trying to solve 1 - 3 cos x = sin^2 x for whatever x is, then you are not talking about an inverse function.

true or false questions: a)The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. b) A sinusoidal function can be differentiated only if the independent variable is measured in radians. c) There are an ...

Algebra
How do you find the inverse of functions? for example how would you find the inverse of y= log8 x

Calculus
We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic functions are any functions that can be made...

Trigonometry
Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then x=f^-1(y). Explain your answer. True or False: For ...

Trigonometry
Having trouble with true/false questions in Trigonometry. They read as follows - True or False: For a trigonometric function, y=f(x), then x=F^-1(y). Explain your answer. True or False: For a one to one function, y=f(x), then x=f^-1(y). Explain your answer. True or False: For ...

Calculus (Derivatives)
What is the derivative of the this functon? g(x) = -500/x, x cannot equal 0. I know that in order to fnd the derivative I need to put the function into the equation for evaluating derivatives as limits. lim as h -> 0 (f(x+h) - f(x))/h I did this, but I am having ...

Algebra 2
Are the functions f and g inverse functions if f(x)=5/3x+1 and g(x)=3(x-1)/5? I need all of the steps on how to determine this. I need this ASAP because this assignment is due tomorrow. Thanks

math
consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2: a. find f(g(x)) b. find g(f(x)) c. determine whether the functions f and g are inverse of each other. I have no clue where to even begin!

calc
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2

convert derivatives of x,y,z, to r, Ɵ,z
convert derivatives of x,y,z, to r, Ɵ,z with chain rule? I want provment rules of converting rectangular derivatives to cylindrical derivatives and and also cylindrical to spherical.I know the rules but I cant prove EQUATIONS.thx alot

math
I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you

Algebra 2
Ok, so I'm trying to find the inverse of each function. We're learning about Inverse Functions and Relations. The problem is f(x)=sqr.root of x/6 The sqr root is confusing me.

algebra
Can someone help with inverse relations and functions? is relation t a function? Is the inverse t a function? chart looks like: x 0 2 4 6 y -10 -1 4 8 If someone could please explain this problem

Functions - math
The function f is such that f(x) = a^2x^2 - ax + 3b for x<=(1/2a), where a and b are constants. 1) For the case where f(-2) = 4a^2 - b +8 and f(-3) = 7a^2 - b + 14, find the possible values of a and b. 2) For the case where a = 1 and b = -1, find an expression for inverse f...

Calculus
solve this equation on the given interval expressing the solution for x in terms of inverse trigonometric functions. 6(cosx)^2-cosx-5=0 on (pie/2, pie)

Pre-Calculus
g(x)= x^2+7 Find the inverse of g(x) and state the domain and range for the inverse of g(x) using interval notation

Calculus
Does f(x)= 1 + cos(x), have an inverse or not, if so, what is the inverse? please explain.

math
Find the derivatives of the following functions. 1.F (x)cotx 2.f (x)=sin (x2+2)

calculus
Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. f(x)=3+e^4−x

calculus (gr 12)
Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)

calculus (gr 12)
Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)

Determine the velocity and acceleration as functions of time, t, for s(t) = 45t − 5t^2, where s(t) represents the distance as a function of time. (Hint: velocity and acceleration correspond to the first and second derivatives of the distance)

pre calculus
If f and g are inverse functions and the point (-3, 5) is on the graph of f, then the point ____ is on the graph of g

Calculus
I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). Therefore the slope of the tangent line at x=...

Calculus
If g(X) = 2+ln(x-5), find the inverse function, (g^(-1))(x) Solution: y = 2+ ln(x-5) e^y = 2 + x - 5 x = e^y + 3 y = e^x + 3 g^(-1) = y = e^x + 3 Is that right? I'm following an example - but don't really get it - how do I determine the domain and range - I know they flip when...

pre calculus
Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. F(x)= ln(8-x) I am totally lost, somebody please help????

calculus
f(x)=sqrt(x-2) what is the inverse of f? I got inverse f(x)= x^2+2 however, you need to specify the domain of x. the answer key says when x=>0 can you please explain why? I thought it would be when x=>2 ?

calculus
f(x)= 3x^7 +2x -9 If g(x)= f inverse of x and g(-4)= 1, what is g'(-4)? I know that f inverse is the same as 1/f'(x) but I'm not sure where to go from there.

pre calculus
Find the inverse of the function below. Graph the function below and the inverse. Determine the domain, range and asymptotes of the function below and the inverse function. Please show all your work. f(x) = 2e^-x + 5 Just looking at this gives me a headache. HELP!

math
find the derivatives, dy/dx, for the following functions : y=(1+sin^2{2 exp (3x)})^5y please help me to solve this assignment. thank's

Calculus
Show that u(x, t) = f(x−ct)+g(x+ct), where c is a constant and f and g have continuous second derivatives, is a solution of the wave equation in one dimension, ie (∂t)^2 u = c^2 ∂x^2 u. Note that this solution to the wave equation consists of two functions ...

Algebra
Given the functions f(x)=x+5/3 and g(x)=1/f^-1(x)+1, find the value of g(3). The first step would first be to find the inverse of x+1, the denominator of the fraction. I think the inverse would be 1-x. And now we have 1/1-x so we can just plu in 3. Right?

Math - Derivatives
How would one take the derivative of "f(x)^[g(x)]? Is there a formula I can follow to differentiate functions like that?

Functions
What is the inverse of h(x)= (1/4x^2)+x ?

Calculus/Derivatives
In addition, can you walk me through how to get the derivatives for these 2 statements, too? a) y = x^5/3 - 5x^2/3 b) y = (the cubed root of the quantity) [(x^2 - 1)^2] Hi there. I need to find the first derivative of this statement. y=x(x+2)^3 I tried the chain rule, but I ...

1. Given f(x)=x^2 and g(x)=x+2, determine in standard form: a)g(f(x)) b)when f(g(x))=g(f(x)) for #1 would the answer for a be x^2+2? 2. Given the functions f(x)=5x+7 and g(x)=√x state the domain of g(x) and g(f(x)) 3. Why is point (a,a) a point on f-1(f(x)) if (a,b) is a...

Calculus
Using inverse trigonometric functions, find a solution to the equation cos(x)=0.2 in the interval 0â‰¤xâ‰¤4Ï€. Then, use a graph to find all other solutions to this equation in this interval. Enter your answers as a comma separated list. Thank you x=

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...

a) determine the derivative of y = sin2x b) determine the derivative of y = 2SinxCosx c) shoe that derivatives in parts a) and b) are equal d) explain why derivatives in parts a) and be should be equal.

math
Find the inverse of each of these functions a)f(x)=x/x+2 b)f(x)=2x/5-x c)f(x)=3x/2x+1

Calculus, only two problems.
If g(x) is the inverse of f(x), g(x)=f^-1(x), such that g(3)=5 and f'(5)=4 what is the value of g'(3)????? :O 2. If g(x)is the inverse of f(x), g(x)=f^-1(x), such that f(3)=15,f(6)=3,f'(3)=-8,and f'(6)=-2. What is the value of g'(3)???????? Calculus--

math
verify that f and g are inverse functions. f(x) = 5x^2 x>(or equal too)0 g(x)= (x+2/5)^1/2

Math
If f and g are inverse functions, f (7) =10 and f (10) = −1 , find g(10).

Math
Which of the following functions has an inverse that is not a function? a. (1,1),(1,2),(3,4) b. (1,2),(1,3),(4,3) c. (1,4),(4,5),(5,6) d. (0,0),(1,1),(2,2)

Math
Which of the following functions is the inverse of the function {(1,2),(3,4),(6,8)}? a. {(6,8),(3,4),(1,2)} b. {(2,1),(4,3),(6,8)} c. {(2,1),(4,3),(8,6)} d. {(2,1),(3,4),(8,6)}***

precal
Which of the following functions is the inverse of the function {(1,2),(3,4),(6,8)}? a. {(6,8),(3,4),(1,2)} b. {(2,1),(4,3),(6,8)} c. {(2,1),(4,3),(8,6)} d. {(2,1),(3,4),(8,6)}

Calculus
show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other? That is the key. i need more info..i know how to find the derivative...but how will that prove my question. Do I need...

pre-cal
How do you work inverse functions alebraically?

calculus
derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?

Derivatives ~ Calculus
If dy/dx = (1 + x)/(xy), x>0, and y=-4 when x=1, then when x=3, y= what?

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

calculus
a)find the first partial derivatives of f(x y)= x √1+y^2 b)find the first partial derivatives of f(x,y)= e^x ln y at the point (0,e)

algebra
Which of the following functions has an inverse that is not a function? y=x y=2x+1 y=x to the second power

MATH
Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

MATH
Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

MATH
Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

MATH HELP
Two functions g and h are defined as : g:x--> 2x+3/x-4 h:x --> 1/x Write expressions for : a) hg(x) b) g inverse 1(x)

College Algebra
verify that the functions of f and g are inverse of each other by showing that f(g(x))=x and g(f(x))=x; f(x)=In(x-1),g(x)=1+e^x

Calculus
Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7

Calculus-derivatives
Determine h'(x) for h(x)= [x/(1-x)]^2

calculus
Anti-Derivatives 2x^6-x^3/x^2

Calculus
Apply the concepts of calculus (limits and derivatives) to describe the graph y = sec(x). Include a quality graph

Did I get these practice questions right? 1. Suppose that f is an even function whose domain is the set of all real numbers. Then which of the following can we claim to be true? ***The function f has an inverse f –1 that is even. The function f has an inverse f –1, but we ...

Pre-Calculus
Operations with Functions write the function below as either a sum/difference/product/quotient of 2 r more functions a. h(x) = x^2+3x+9 How Would I do this? My teacher just did this f(x) = x^2 g(x) 3x+9 ^I don't really understand h(x)=(x+5)(x-3) how would I do this one? If h(x...

Calculus
Math questions, please help me? :(? Find the composite functions f o g and g o f for the given functions. f(x) = 10^x and g(x) = log x State the domain and range for each: f(x) = 4x + 1 and g(x) = x^2 f(x) = sin x and g(x) = x^2 - x + 1 f(x) = 10^x and g(x) = log x If f = {(-2...

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