Question

# Derivative of y=(sin x)2 with respect to x will be

A
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B
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C
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D
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Solution

## The correct option is D All the formulae mentioned for the derivative of standard functions hold true only when the variable is x itself, not for any other function of x. To make it more clear let’s take lnx as the function. Its derivative with respect to x as we know will be 1x, but the derivative of lnsinx with respect to x will not be 1sinx. Rather it will be 1sinx multiplied by d(sinx)dx. Yes the derivative of lnsinx with respect to sinx will be 1sinx but not with respect to x In this question the function is of the form of xn. The only difference is that it has sinx at the place of x. So we will use chain rule. .dydx=dyd(sinx)×d(sinx)dx dyd(sinx)=2sinx d(sinx)dx=cosx So dydx=2sinxcosx Also you can write the function as sinx.sinx and try to solve it using product rule.

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