If #f(x)= (5x -1)^3-2 # and #g(x) = e^x #, what is #f'(g(x)) #?

2 Answers
Apr 13, 2018

Answer:

#15e^x(5e^x-1)^2#

Explanation:

First, let's find #f(g(x))#

#(5(e^x)-1)^3-2#

Now we take the derivative of this:

Power rule

#f'(g(x)) = 3(5e^x-1)^2#

We need to apply the power rule and take the derivative of what's inside the parentheses

#(5e^x-1)' = 5e^x#

So our final answer is #f'(g(x)) = 3(5e^x-1)^2 xx 5e^x# or #15e^x(5e^x-1)^2#

Apr 13, 2018

Answer:

#=>f'(g(x)) = 15(5e^x - 1)^2#

Explanation:

#f(x) = (5x - 1)^3-2#

#f(g(x)) = (5e^x - 1)^3 - 2#

#f'(g(x)) = d/(dx)[(5e^x-1)^3-2]#

#=>f'(g(x)) = d/(dx)(5e^x-1)^3 -d/(dx)(2)#

#=>f'(g(x)) = 15e^x(5e^x-1)^2#

Hence, the solution is:

#=>f'(g(x)) = 15e^x(5e^x - 1)^2#