If $f (x) = 3 x^{3} - 2$ $f(x)= 3x^3-2$ and $g (x) = e^{x}$ $g(x) = e^x$ , what is $f'(g(x))$ ?

Question

If $f (x) = 3 x^{3} - 2$ $f(x)= 3x^3-2$ and $g (x) = e^{x}$ $g(x) = e^x$ , what is $f'(g(x))$ ?

1 Answer

Impact of this question

1463 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-21T18:37:33

$f'(g(x))=9e^(3x)$

Explanation:

Before differentiating we require to find f(g(x)).

$rArrf(g(x))=f(e^x)=3(e^x)^3-2=3e^(3x)-2$

differentiate using the $color(blue)"chain rule"$

$rArrf'(g(x))=3e^(3x).d/dx(3x)=9e^(3x)$

Science

Math

Humanities

... and beyond

If $f (x) = 3 x^{3} - 2$ $f(x)= 3x^3-2$ and $g (x) = e^{x}$ $g(x) = e^x$ , what is $f'(g(x))$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

If f(x)= 3x^3-2 f(x)=3x3−2f(x)= 3x^3-2 and g(x) = e^x g(x)=exg(x) = e^x , what is f'(g(x)) f'(g(x)) ?

1 Answer

Explanation:

Related questions

Impact of this question

If $f (x) = 3 x^{3} - 2$ $f(x)= 3x^3-2$ and $g (x) = e^{x}$ $g(x) = e^x$ , what is $f'(g(x))$ ?