Question

determine the derivative with respect to x of y=e^9x^3+4x

Answer 1

\[y=e ^{9x ^{3}+4x}\]

Answer 2

You need to apply the chain rule, you have the function 9x^3+4x "inside" the function e^x. So you need to apply this rule:
\[\frac{d}{dx}f(g(x))=f'(g(x))*g'(x)\]
Here:
\[f(x)=e^x; g(x)=9x^3+4x \implies f'(x)=e^x \implies f'(g(x))=e^{9x^3+4x}; \]
\[g'(x)=27x^2+4; \implies \frac{d}{dx}e^{9x^3+4x}=(27x^2+4)e^{9x^3+4x}\]

Answer 3

Also note:
\[f(x)=e^x; g(x)=9x^3+4x \implies f(g(x))=e^{9x^3+4x} \]
Which is your function which is why this rule is applied and works.

Answer 4

ok im with you i was confused but i just got it lol thanks