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

1 Answer
Mar 17, 2016

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

Explanation:

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.