Question

How do I take the derivative of (integral(e^-s^2 ds) from 0 to t?

Answer 1

Do you know the fundamental theorem of calculus?

Answer 2

would it simply be e^(-s^2)?

Answer 3

Yes indeed.

Answer 4

Okay good thanks just reviewing

Answer 5

but wait you don't take 0 or t into account?

Answer 6

the integration from 0 to t I meant

Answer 7

No. The Theorem says (minus some technicalities) the following.

Let F(x) be the function
\[F(x) = \int\limits_{a}^{x} f(t) \ dt\]
for some function f.

Then the derivative of F exists and
\[\frac{dF}{dx}(x) = f(x)\]

Notice that this result is completely independent of a.

Answer 8

You need to use the second fundamental theorem of calculus