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Answer 1 · 2017-07-01T21:35:51

#(df(e^tan(0)))/dx = 5#

#(df(e^tan(x)))/dx = sec^2(x)e^tan(x)f'(e^tan(x))#

Let #x = 0#:

#sec^2(0)e^tan(0)f'(e^tan(0))#

Use the fact that #sec^2(0) = 1#:

#e^tan(0)f'(e^tan(0))#

Use the fact that #tan(0) = 0#:

#e^0f'(e^0)#

Use the fact that #e^0 = 1#:

#1f'(1)#

We are given that #f'(1) = 5#

Therefore,

#(df(e^tan(0)))/dx = 5#