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Question

Find the derivative : x2·cosπ4sinx


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Solution

Solution:

The quotient rule of differentiation is,

uv'=u'v-vu'v2

In the given function, u=x2,v=sinx

Lety=cosπ4x2sinxdydx=cosπ4sinx·ddxx2-x2·ddxsinxsin2xdydx=cosπ4sinx·2x-x2·cosxsin2xdydx=122x·sinx-x2·cosxsin2x

Hence, the required expression is dydx=122x·sinx-x2·cosxsin2x.


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