Derivatives of Functions

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July 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.
July 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 $u=-x^9$
July 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
July 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
July 13th 2011, 06:40 AM
StarDancer19

Re: Derivatives of Functions

Sorry about that, but the question I am asking is the first suggestion you had.
July 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
July 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 $\frac{df}{dx}= \frac{df}{du}\frac{du}{dx}$ .