Question

Differencate
$y = \sqrt{sin \: log \: e \: \sqrt{x} }$
by chain rule. ​

Answer 1

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Answer 2

SOLUTION

Given f(x)=sin(cosx)−−−−−−−−√

Differentiating it w.r.t x

Apply chain rule  

[u(x)n]′=n.u(x)n−1.u′(x)

f′(x)=12sin12−1(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)−−−−−−−−√