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The derivative of sin^2x with respect to...

The derivative of `sin^2x` with respect to `cos^2x` is equal to....

A

`tan^2x`

B

`tanx`

C

`-tanx`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Let `u=sin^2xxand v=cos^2x`
On differenting w.r.t.x, respectively , we get
`(du)/(dx)=2sinx cos x`
and `(dv)/(dx)=-2sinxcosx`
`therefore (du)/(dv)=(du//dx)/(dv//dx)=(2sinxcosx)/(-2sinxcosx)=-1`
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