Saturday

March 28, 2015

March 28, 2015

Posted by **AHKSIJ** on Wednesday, December 7, 2011 at 12:08pm.

- calculus -
**Steve**, Wednesday, December 7, 2011 at 1:35pmf = g(e^2x)

f' = 2e^2x g'

f'' = 4e^2xg' + 2e^2xg''

example:

g(x) = x sinx

f(x) = g(e^2x) = e^2x sin(e^2x)

g' = sinx + xcosx

g'' = cosx + cosx - xsinx

= 2cosx - xsinx

f' = 2e^2x sin(e^2x) + e^2xcos(e^2x)*2e^2x

= 2e^2x(sin(e^2x) + e^2x cos(e^2x))

Letting g(e^2x) = g(u)

f' = 2e^2x g'(u)

I have expanded out

4e^2xg'(u) + 2e^2xg''(u)

and it checks out. Have lots of blank paper!

**Answer this Question**

**Related Questions**

calculus - Calculate f" for f(x)=g(e^(2x)), where g is a function defined for ...

calculus - Use the function defined below to calculate the indicated derivative...

Math - The twice–differentiable function f is defined for all real numbers and ...

math - Consider the function defined below. y = 2t3 - 4t2 + 3 (a) Calculate the ...

domain - Find the domains of f and f' 1, f(x) = xe^x 2. f(x) = x^(3/5) 3. f(x...

Pre-Calculus - A rectangle is bounded by the x-axis and the semicircle y = &#...

Applied Calculus - Find the first and second derivative of the function: x/(7x+...

math - Let the Function a @ b be defined as 3a + 2b for all real numbers a and b...

math 116 - What is the difference between domain and range? The domain of a ...

calculus - 1. Let f be the function that is defined for all real numbers x and ...