[math] \frac{dcos(x)}{dsin(x)}=? [/math]

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[math] \frac{dcos(x)}{dsin(x)}=? [/math]

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>>7848404

>The derivative of cos(x)

>With respect to sin(x)

0.

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>>7848410

elaborate

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>>7848404

what does this mean? define your terms. it's probably infinite if you define it well, since the linear part of sin is x and the linear part of cos is 1

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>>7848404

tan(x)

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>>7848404

dsin(x) = cos(x)*dx

dcos(x) = -sin(x)*dx

dcos(x)/dsin(x) = -tan(x)

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>>7848404

the d cancels out and you get cot(x)

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>>7848477

You were so close...

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>>7848488

I was right.

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>>7848404

Let [math]y = \sin x[/math] so [math]\frac{d\cos x}{d\sin x} = \frac{d \cos \arcsin y}{d y}[/math]

Input into wolfram alpha http://www.wolframalpha.com/input/?i=derivative+of+cos%28arcsin%28x%29%29 then substitute back. Result is [math]-\tan x[/math].

This works for all derivable f(x),g(x), you can check it.

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>>7848859

[math]tan(x) = \frac{sin(x)}{cos(x)}[/math]

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>>7848896

There's a minus sign that comes from differentiating cos(x)

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