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The derivative of sin (x^(3)) w.r.t. c...

The derivative of ` sin (x^(3)) ` w.r.t.` cos(x^(3))` is

A

`- tan (x^(3))`

B

`tan (x^(3))`

C

`-cot (x^(3))`

D

`cot (x^(3))`

Text Solution

Verified by Experts

The correct Answer is:
C
Let ` u = sin x^(3) and v = cos x^(3)` .
On differentiating both functions w.r.t.x, we get
`(du)/(dx) = cos x^(3) "and " (dv)/(dx) = - sin x^(3) . 3x^(2)`
` therefore (du)/(dv) = (du//dx)/(dv//dx) = (3x^(2) cos x^(3))/(-3x^(2) sin x^(3)) = - cot x ^(3)`.
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