Answer:
[(sec^2)(x)]. [e^tan(x)]
Or
[e^(tan(x))]/[(cos^2)(x)].
Step-by-step explanation:
d/dx(e^tan(x))
From the low:
[(d/du)(e^u)]=[(d/du)(u)]. [ln(e)]. [e^u]
=[(sec^2)(x)]. [e^(tan(x))]. [ln(e)]
=[(sec^2)(x)]. [e^(tan(x))]
or
[e^(tan(x))]/[(cos^2)(x)].
Because
(cos^2)(x)=1 / (sec^2)(x)
