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Question

Differentiate w.r.t. x :
f(x)=sin(cosx)

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Solution

Given f(x)=sin(cosx)

Differentiating it w.r.t x

Apply chain rule

[u(x)n]=n.u(x)n1.u(x)

f(x)=12sin121(cosx).dd[sin(cosx)]

Apply differentiation rule
[sin(u(x))]=[cos(u(x))].u(x)

f(x)=cos(cosx)(sinx)2sin(cosx)

f(x)=sinxcos(cosx)2sin(cosx)

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