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December 10, 2016

Search: Calculus (Derivatives of Inverse Functions)

Number of results: 20,043

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.
March 15, 2012 by Mooch

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?
October 23, 2011 by Josh

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...
July 30, 2007 by COFFEE

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, ...
September 23, 2011 by Scooby16

calculus
Find the derivatives of the functions k(x)=(x^3+e^x)^4
February 11, 2013 by Joe

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
January 10, 2008 by Anonymous

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
March 31, 2013 by Matthew

Advanced Algebra
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 ...
November 15, 2014 by Keith

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.
June 18, 2013 by Robin

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!
September 9, 2007 by Joe

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 ...
January 31, 2015 by Aria

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
September 4, 2006 by kris!

Calculus
[Inverse Functions] f(x)= 5cos(x)sin^(-1)(x) f'(x)=?
October 7, 2009 by Z32

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.
April 30, 2013 by Thomas

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.
November 28, 2016 by Anonymous

Advanced Functions 12
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?
September 17, 2016 by y=1/0

Calculus III
Derivative of Inverse Trigonometric Functions f(x) = sin(arccos(4x)) What is f'(x)?
January 22, 2008 by Sean

Calculus III
Derivative of Inverse Trigonometric Functions f(x) = cos(arcsin(2x)) What is f'(x)?
January 22, 2008 by Sean

Calculus
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2 the sqrt is just over t.
February 4, 2013 by Mike

Calculus
Find the first and second derivatives of the given functions. y=¡î(x©÷+1) y'=x(x©÷+1)^(-1/2) y"=[1(x©÷+1)^(-1/2)]-[(1/2)[(x©÷+1)^(-3/2)](2x)(x)] y"=[(x©÷+1)^(-1/2)]-[(x©÷)(x©÷+1)^(-3/2)] Is the second derivative right?
November 10, 2009 by sh

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 ...
February 15, 2009 by joey

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...
November 17, 2014 by Lily

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)
April 16, 2013 by Tima

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!
February 5, 2012 by Elaine

Please HELP! Calculus (Implicit functions)
Find the inverse of the function y = (square root x) + 4x , then solve for its 1st order derivative.
April 12, 2016 by Wawen

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.
July 29, 2009 by Alicia

Inverse functions
Solve for y to determine the inverse y=2-(1/2x)
July 23, 2010 by Nada

Inverse Functions
Given that g is the inverse function of f, and f(3)=4, and f'(3)=5, then g'(4)= ?
June 5, 2012 by Ellen

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
March 7, 2012 by maggie

Math - Calculus 1
Approximate using derivatives. (Must show work using derivatives!) Do not use a calculator: (1.1)^4 - (1.1)^2
October 7, 2016 by James

Pre Calculus
Inverse functions find the value If f(x)=1/x, find f^-1 (2)
October 22, 2011 by Josh

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 ...
October 20, 2006 by Jen

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.
February 26, 2007 by fiza

calculus please help asap
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 ...
October 31, 2014 by Tina

Algebra
How do you find the inverse of functions? for example how would you find the inverse of y= log8 x
May 1, 2011 by Kenya

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...
September 13, 2007 by Kelly

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 ...
March 24, 2011 by Veronica

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 ...
March 24, 2011 by Veronica

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 ...
November 1, 2011 by Mishaka

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
May 25, 2011 by Brandon

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!
March 23, 2013 by marie

calc
find the derivatives of the given functions. g(t)=sqrt t(1+t)/t^2
February 5, 2013 by Jake

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
December 1, 2011 by parsa

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
October 9, 2008 by Sam

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.
September 17, 2012 by claire

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
December 10, 2012 by lee

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...
October 15, 2016 by Desperately seeking help

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)
October 10, 2011 by Josh

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
April 26, 2016 by Juniper

Calculus
Does f(x)= 1 + cos(x), have an inverse or not, if so, what is the inverse? please explain.
February 15, 2011 by Carrie

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
September 27, 2013 by Miriam

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)
April 16, 2013 by Alexandra

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)
April 17, 2013 by HELP MEE

Grade 12 Calculus
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)
April 15, 2013 by alex

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
October 10, 2011 by vedo

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=...
March 31, 2009 by Lauren

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...
September 3, 2016 by Linda

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????
April 24, 2013 by trish

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 ?
December 18, 2013 by Anonymous

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.
February 21, 2012 by k

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!
December 20, 2011 by Michelle

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
August 20, 2012 by deel

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 ...
September 30, 2015 by Margo

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?
November 4, 2014 by Trish Goal

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?
January 28, 2009 by Anonymous

Functions
What is the inverse of h(x)= (1/4x^2)+x ?
October 5, 2012 by lola

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 ...
March 14, 2007 by Amy

advanced functions/precalculus
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...
January 13, 2014 by Diane

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...
September 14, 2016 by Mary

Calculus grade 12
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.
April 12, 2012 by Julie

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
October 17, 2013 by jason

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--
March 23, 2010 by JakeT

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
January 26, 2011 by Amanda

Math
If f and g are inverse functions, f (7) =10 and f (10) = −1 , find g(10).
October 12, 2011 by Caprice

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)
November 17, 2015 by Kaai97

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)}***
November 17, 2015 by Kaai97

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...
April 5, 2007 by Amy

pre-cal
How do you work inverse functions alebraically?
September 20, 2007 by chris

calculus
derivatives. f(x)=(1/-7x^12) f'(2)=? f'(-1)=?
January 18, 2008 by mike

Derivatives ~ Calculus
If dy/dx = (1 + x)/(xy), x>0, and y=-4 when x=1, then when x=3, y= what?
June 5, 2012 by Hannah

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
October 22, 2011 by Yousef

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)
March 11, 2012 by maria

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
May 25, 2011 by Loren

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)
September 7, 2011 by Nelly

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)
September 7, 2011 by Nelly

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)
September 7, 2011 by Nelly

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)
September 8, 2011 by Nelly

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
January 1, 2012 by Jennifer

Calculus
Compute the derivatives of : f(x)= x^7 + 7^x+ 7^7
November 22, 2010 by JJ

Calculus-derivatives
Determine h'(x) for h(x)= [x/(1-x)]^2
February 20, 2012 by Jessi

calculus
Anti-Derivatives 2x^6-x^3/x^2
December 11, 2015 by Jason

Calculus, check my answers, please! 3
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 ...
October 2, 2013 by Samantha

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...
September 26, 2012 by Shreya

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...
September 2, 2013 by Britt

Pre-Calculus/Calculus
I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the ...
July 1, 2008 by Molly

Calculus
Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to come out as cos(y)^2, which I know can be ...
October 21, 2006 by Tracy

Math-Derivitives
if f(x)=x^3+5x, then f'(2)= if f(x)=cos(2x), then f'(pi/4) derivatives and anti derivatives please help
March 23, 2010 by AdrianV

calculus
f(x) = (x+2)/(x+6) What is f^(-1)(-6)? (what is f inverse of -6) I found f' which was [(x+6)-(x+2)]/(x+6)^2 I set the function equal to -6 and found x to be -30/7. Used the formula to find inverse function: 1/f'(f^(-1)(-6)) So I replaced f^(-1)(-6) with -30/7 and then the new ...
August 19, 2010 by Pegs

Math
What are the connections to word problems for direct and Inverse Variations and why are they functions?
May 31, 2008 by Anonymous

Math
What are the connections to word problems for direct and Inverse Variations and why are they functions?
May 31, 2008 by Anonymous

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