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$\frac{dcos(x)}{dsin(x)}=?$
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$\frac{dcos(x)}{dsin(x)}=?$
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>>7848404
>The derivative of cos(x)
>With respect to sin(x)

0.
>>
>>7848410
elaborate
>>
>>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
>>
>>7848404
tan(x)
>>
>>7848404
gibberish

literally this:

>>7848410
>>
>>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 $y = \sin x$ so $\frac{d\cos x}{d\sin x} = \frac{d \cos \arcsin y}{d y}$

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

This works for all derivable f(x),g(x), you can check it.
>>
>>7848859
$tan(x) = \frac{sin(x)}{cos(x)}$
>>
>>7848896
There's a minus sign that comes from differentiating cos(x)

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