- #1

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f(x) = cos pi*x

I know f'(x) cos x = - sin x but what about that pi?

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- Thread starter IceColdCola19
- Start date

- #1

- 1

- 0

f(x) = cos pi*x

I know f'(x) cos x = - sin x but what about that pi?

- #2

- 506

- 1

Are you familiar with the chain rule ?

- #3

James R

Science Advisor

Homework Helper

Gold Member

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[tex]\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}[/tex]

Take y = cos u

then you know that dy/du = -sin u.

Now put u = nx, for n a constant.

You know that du/dx = n

Now consider:

y = cos nx

Put u = nx, so that y = cos u. Then the chain rule tells us:

[tex]\frac{dy}{dx} = \frac{dy}{du} \frac{du}{dx}[/tex]

[tex]= (-\sin u)(n)[/tex]

[tex]= -n\sin nx[/tex]

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