anonymous 2 years ago F(x)= ∫cos(e^t)dt top limit ln(x) bottom limit pi, what is the derivative of F(x)

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1. anonymous

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.

2. anonymous

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

3. anonymous

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