[math] \frac{dcos(x)}{dsin(x)}=? [/math]
>>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
dsin(x) = cos(x)*dx
dcos(x) = -sin(x)*dx
dcos(x)/dsin(x) = -tan(x)
>>7848404
the d cancels out and you get cot(x)
>>7848477
You were so close...
>>7848488
I was right.
>>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.
>>7848859
[math]tan(x) = \frac{sin(x)}{cos(x)}[/math]
>>7848896
There's a minus sign that comes from differentiating cos(x)
