# Derivatives of Functions

• Jul 13th 2011, 06:31 AM
StarDancer19
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.
• Jul 13th 2011, 06:35 AM
Siron
Re: Derivatives of Functions
You have to be clearer.
Is it:
$y=4-7e^{(-x^9)}$? ...
If yes, use the chain rule.
The derivative of $e^u=e^u.D(u)$
Let $u=-x^9$
• Jul 13th 2011, 06:38 AM
CaptainBlack
Re: Derivatives of Functions
Quote:

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 $4-7e^{-x^9}$ or $4-7(e^{-x})^9$ or something else.

CB
• Jul 13th 2011, 06:39 AM
StarDancer19
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
• Jul 13th 2011, 06:40 AM
StarDancer19
Re: Derivatives of Functions
• Jul 13th 2011, 06:43 AM
e^(i*pi)
Re: Derivatives of Functions
$\dfrac{d}{dx}f[g(x)] = f'[g(x)] \times g'(x)$

In your example you have $f(x) = -7e^{g(x)} \text{ and } g(x) = -x^9$

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Alternatively:

$\dfrac{dy}{dx} = \dfrac{dy}{du} \cdot \dfrac{du}{dx}$

You have $y(u) = -7e^u \text{ and } u(x) = -x^9$

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Both notations depict the chain rule so pick whichever is easier to understand
• Jul 13th 2011, 07:10 AM
HallsofIvy
Re: Derivatives of Functions
Quote:

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 $u= -x^9$ then $f(x)= 4- 7e^{-x^9}$ becomes $f(u)= 4-7e^u$. Can you find df/du?

And what is du/dx?

The chain rule says $\frac{df}{dx}= \frac{df}{du}\frac{du}{dx}$.