# calculus

posted by .

Calculate f" for f(x)=g(e^(2x)), where g is a function defined for all real numbers & g admits second order derivative.

• calculus -

f = 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!

## Similar Questions

1. ### domain

Find the domains of f and f' 1, f(x) = xe^x 2. f(x) = x^(3/5) 3. f(x) = x/(x-2) TIA 1) R 2) It's the interfal from zero to infinity for f but for f' it is this inteval with zero excluded, because unlike f, f' is singular at zero. 3) …
2. ### math

Let the Function a @ b be defined as 3a + 2b for all real numbers a and b. If u and v are real #'s for which u and v = v @ u = 20. What is the value of 2u @ 3V?
3. ### math

Consider the function defined below. y = 2t3 - 4t2 + 3 (a) Calculate the second derivative. y '' = (b) Calculate the third derivative. y ''' =
4. ### calculus

Use the function defined below to calculate the indicated derivative. f(t)= 4/(t^3)+3 what is f''(2) (second derivative) Need help!!
5. ### Pre-Calculus

A rectangle is bounded by the x-axis and the semicircle y = √36 â€“ x2, as shown in the figure below. Write the area A of the rectangle as a function of x, and determine the domain of the area function. A = all real numbers except …
6. ### calculus

Calculate f" for f(x)=g(e^(2x)), where g is a function defined for all real numbers & g admits second order derivative.
7. ### 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 …
8. ### Math

The twiceâ€“differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a constant. …
9. ### 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 …
10. ### Math

Let the function a@b be defined as 3a + 2b for all real numbers a and b. If u and v are real numbers for which u@v =v@u = 20, what is the value of 2u@3v?

More Similar Questions