Question

I have the answer cansomeone please tell me what they got...
Find the derivative of
k(x)=tan(e^x)

Answer 1

Let \[u=e^x\]then \[k(x) = \tan(u)\]By chain rule we can do \[\frac{ dk(x) }{ dx }= \frac{ dk(x) }{ du }\frac{ du }{ dx }\] So we know that \[\frac{ du }{ dx }= e^x\] by definiteion of the exponential function. We also know that \[\frac{ dk(x) }{ du }= \sec^2(u)\] which is easily shown byt the quotient rule (let tan(x) = sin(x)/cos(x) and diff it that way). So overall we have that \[\frac{ dk(x) }{ dx }= e^xsec^2(e^x)\] Hope this helped:)