Question

F(x)= ∫cos(e^t)dt top limit ln(x) bottom limit pi, what is the derivative of F(x)

Answer 1

When the lower limit is a constant it drops out when taking the derivative, so it doesn't matter whether it's pi or 0 or any other constant. The question is how to deal with ln(x) as the upper limit. How about this:\[\cos(e^{\ln x})\frac{ 1 }{ x }=\frac{ \cos x }{ x }\]because e^(ln x) is just x.

Answer 2

Thans a lot, but one more question where did you get 1/x from?

Answer 3

We substituted ln x for t, so we need to substitute d(ln x) for dt.