Question

derivative of √sin√x

Answer 1

Answer :

Let, y = √(sin√x)

or, y = (sin√x)^(1/2)

Now, differentiating with respect to x, we get

dy/dx

= 1/2 (sin√x)^(1/2 - 1) d/dx (sin√x)

= 1/2 (sin√x)^(-1/2) (cos√x) d/dx (√x)

= 1/2 1/√(sin√x) (cos√x) d/dx {x^(1/2)}

= 1/2 1/√(sin√x) (cos√x) 1/2 x^(1/2 - 1)

= 1/2 1/√(sin√x) (cos√x) 1/2 x^(-1/2)

= (1/2 × 1/2) √(sin√x) (cos√x) 1/(√x)

= 1/4 √(sin√x) (cos√x) 1/(√x)

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