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Question

If y=[x+x2+a2]n,then dydx is equal to


A

nyx2+a2

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B

nyx2+a2

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C

nxx2+a2

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D

nxx2+a2

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Solution

The correct option is A

nyx2+a2


Using chain rule, we have
dydx=ddx[{x+x2+a2}n]
=n{x+{x2+a2}}n1.ddx{x+x2+a2}
=n{x+x2+a2}n1{x2+a2+xx2+a2}
=n{x+x2+a2}nx2+a2=nyx2+a2


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