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

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Answer 1 · 2018-07-09T03:45:53

#e^x sec^2(e^x)#

Given: #f(x) = tan(e^x)#

Use the derivative rules: #d/dx(tan x) = sec^2 x; " "d/dx(e^x) = e^x#

Using the chain rule:

Let #u = e^x; " "u' = e^x#

#f(u) = tan u#

#f'(u) = u' sec^2 u#

#f'(x) = e^x sec^2 (e^x)#