1. ## Derivatives 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.

2. ## Re: 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 $\displaystyle u=-x^9$

3. ## Re: Derivatives of Functions

Originally Posted by StarDancer19
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.
It would really help if you put in parentheses so we knew if you meant $\displaystyle 4-7e^{-x^9}$ or $\displaystyle 4-7(e^{-x})^9$ or something else.

CB

4. ## Re: 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

6. ## 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

7. ## Re: Derivatives of Functions

Originally Posted by StarDancer19
Sorry about the clearness. It is: 4- [7e^(-x^9)]

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

That I need help on is actually seeing the work of the rest
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 $\displaystyle \frac{df}{dx}= \frac{df}{du}\frac{du}{dx}$.