Find the derivative of the function. f(t) = tan(e^5t) + e^(tan (5t))?

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Found it! It was stuck in your notes.

This is a great chain-rule problem
d/dx a(x) = a'(x)
d/dx a(b(x)) = a'(b(x)) * b'(x)
d/dx a(b(c(x))) = a'(b(c(x))) * b'(c(x)) * c'(x)
d/dx a(b(c(d(x)))) = a'(b(c(d(x)))) * b'(c(d(x))) * c'(d(x)) * d'(x)

And so on

d/dt tan(e^(5t)) =>
sec(e^(5t))^2 * e^(5t) * 5

d/dt e^(tan(5t)) =>
5 * sec(5t)^2 * e^(tan(5t))