Differential of cos(piy) Watch

Dinasaurus
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#1
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How do I differentiate cos(piy)?

Should I use chain rule??
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Cerdic
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The differential of any cos(f(x)) is -f'(x)sin(f(x))

Eg d(cos(2x))/dx = -2sin(2x)
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Dinasaurus
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(Original post by Cerdic)
The differential of any cos(f(x)) is -f'(x)sin(f(x))

Eg d(cos(2x))/dx = -2sin(2x)
So it's just -pisin(y)?

No dy/dx or anything?
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Cerdic
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(Original post by Dinasaurus)
So it's just -picos(y)?

No dy/dx or anything?
You haven't said what you're differentiating with respect to, but assuming it's y, then the answer would be -\pi sin(\pi y)
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B_9710
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(Original post by Dinasaurus)
So it's just -pisin(y)?

No dy/dx or anything?
 \displaystyle \frac{d}{dx} \left [ \cos(\pi y) \right ] = -\pi \sin(\pi y)\frac{dy}{dx} .
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Cerdic
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(Original post by B_9710)
 \displaystyle \frac{d}{dx} \left [ \cos(\pi y) \right ] = -\pi \sin(\pi y)\frac{dy}{dx} .
Or that if you're differentiating wrt x
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Dinasaurus
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(Original post by B_9710)
 \displaystyle \frac{d}{dx} \left [ \cos(\pi y) \right ] = -\pi \sin(\pi y)\frac{dy}{dx} .
Where does that dy/dx come from? What method would be used to do this or is this just something I am expected to know?
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B_9710
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(Original post by Dinasaurus)
Where does that dy/dx come from? What method would be used to do this or is this just something I am expected to know?
Well  \displaystyle \frac{d}{dx} \left [\cos(\pi y) \right ]= \frac{dy}{dx} \frac{d}{dy} \left [ \cos(\pi y) \right ]
See how the dy on the top and bottom kind of cancel out leaving just d/dx (cosπy). That's what you do. Differentiate the function with respect to y then multiply by dy/dx.
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