If $f (x) = {(5 x - 1)}^{3} - 2$ $f(x)= (5x -1)^3-2$ and $g (x) = e^{x}$ $g(x) = e^x$ , 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:

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

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