Question

find the derivative of cos[sin(√x)] with respect to x​

Answer 1

Answer:

[ ( cos √ x ) ( - sin ( sin √ x ) ) ] / [ 2 √ x ]

Step-by-step explanation:

Given :

y = cos [ sin ( √ x ) ]

We are asked to find y' :

Applying chain rule :

Diff. w.r.t  x :

y' = - sin [ sin ( √ x ) ]  [ sin ( √ x ) ]'

y' = - sin [ sin ( √ x ) ] [ ( cos ( √ x ) ] [ ( √ x ) ]'

y' = ( - sin [ sin ( √ x ) ] [ ( cos ( √ x ) ] ) /  2 √ x

y' = [ ( cos √ x ) ( - sin ( sin √ x ) ) ] / [ 2 √ x ]

Hence we get required answer!

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Find derivative of ( x² + 1 ) ( 2 cos x + 3 sin x ) with respect to x.

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