How do you differentiate #f(x)=ln(cos(e^(x) )) # using the chain rule?

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Answer 1 · 2016-03-17T10:49:19

#dy/dx=-tane^x*e^x#

So, we got three functions here:

#ln(cos(e^x))#

#cos(e^x)#

and

#e^x#

Let #y=ln(cos(e^x))#

differentiating w.r.t. #x#

#dy/dx=d/dxln(cos(e^x))#

#dy/dx=1/cos(e^x)*d/dxcos(e^x)#

#dy/dx=-1/cos(e^x)*sin(e^x)*d/dxe^x#

#dy/dx=-1/cos(e^x)*sin(e^x)*e^x#

#dy/dx=-sin(e^x)/cos(e^x)*e^x#

#dy/dx=-tane^x*e^x#

This will be the differentiated function.