The question is asking to find the derivative of the function:
y=4-7e^-x^9
I am confused because there are so many exponents. It would really help to see the work with the answer.
$\displaystyle \dfrac{d}{dx}f[g(x)] = f'[g(x)] \times g'(x)$
In your example you have $\displaystyle f(x) = -7e^{g(x)} \text{ and } g(x) = -x^9$
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Alternatively:
$\displaystyle \dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}$
You have $\displaystyle y(u) = -7e^u \text{ and } u(x) = -x^9$
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Both notations depict the chain rule so pick whichever is easier to understand
What that tells me is that you have no idea how to use the chain rule!
You don't use the chain rule to "find that u= -x^9".
If $\displaystyle u= -x^9$ then $\displaystyle f(x)= 4- 7e^{-x^9}$ becomes $\displaystyle f(u)= 4-7e^u$. Can you find df/du?
And what is du/dx?
The chain rule says $\displaystyle \frac{df}{dx}= \frac{df}{du}\frac{du}{dx}$.