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

Question

anonymous · Answer

$$y=e ^{9x ^{3}+4x}$$

anonymous · Answer

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:
$$f(x)=e^x; g(x)=9x^3+4x \implies f'(x)=e^x \implies f'(g(x))=e^{9x^3+4x}; $$
$$g'(x)=27x^2+4; \implies \frac{d}{dx}e^{9x^3+4x}=(27x^2+4)e^{9x^3+4x}$$

anonymous · Answer

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.

anonymous · Answer

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