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

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Answer 1 · 2018-04-13T18:20:27

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

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

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

Now we take the derivative of this:

#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#

Answer 2 · 2018-04-13T18:20:55

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

#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#