compute the following

(a) d/dx[ integrate(x to e^(x^2)) (ln(t))dt]

(b) d/dx[ int (2 to e^(x^2) )(ln(t))dt]

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- Nov 23rd 2006, 05:59 AMgracyfundamental theorem of calculus
compute the following

(a) d/dx[ integrate(x to e^(x^2)) (ln(t))dt]

(b) d/dx[ int (2 to e^(x^2) )(ln(t))dt] - Nov 23rd 2006, 06:26 AMtopsquark
- Nov 23rd 2006, 06:29 AMThePerfectHacker
Again I am so angry that you do not mention a function on what domain.

But since,

this function is on the entire real domain.

You have,

You can consider this function as a composition of functions.

Then,

Since, is differenciable everywhere and is differenciable for for that is the fundamental theorem. Thus,

Thus,

for . - Nov 23rd 2006, 06:30 AMtopsquark