What is the derivative of #f(x) = sin (cos (tanx) )#?

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1s2s2p Share
Mar 13, 2018

Answer:

#f'(x)=-sec^2xsin(tanx)cos(cos(tanx))#

Explanation:

#f(x)=sin(g(x))#
#f'(x)=g'(x)cos(g(x))#

#g(x)=cos(h(x))#
#g'(x)=-h'(x)sin(h(x))#

#h(x)=tan(x)#
#h'(x)=sec^2x#

#g'(x)=-sec^2xsin(tanx)#
#g(x)=cos(tanx)#

#f'(x)=-sec^2xsin(tanx)cos(cos(tanx))#

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