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.

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- Jul 13th 2011, 06:31 AMStarDancer19Derivatives of Functions
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. - Jul 13th 2011, 06:35 AMSironRe: Derivatives of Functions
You have to be clearer.

Is it:

$\displaystyle y=4-7e^{(-x^9)}$? ...

If yes, use the chain rule.

The derivative of $\displaystyle e^u=e^u.D(u)$

Let $\displaystyle u=-x^9$ - Jul 13th 2011, 06:38 AMCaptainBlackRe: Derivatives of Functions
- Jul 13th 2011, 06:39 AMStarDancer19Re: Derivatives of Functions
Sorry about the clearness. It is: 4- [7e^(-x^9)]

I understand how to use the chain rule to find that u=-x^9

What I need help on is actually seeing the work of the rest - Jul 13th 2011, 06:40 AMStarDancer19Re: Derivatives of Functions
Sorry about that, but the question I am asking is the first suggestion you had.

- Jul 13th 2011, 06:43 AMe^(i*pi)Re: Derivatives of Functions
$\displaystyle \dfrac{d}{dx}f[g(x)] = f'[g(x)] \times g'(x)$

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 - Jul 13th 2011, 07:10 AMHallsofIvyRe: Derivatives of Functions
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 $\displaystyle \frac{df}{dx}= \frac{df}{du}\frac{du}{dx}$.