Still a little confused

[Marierose]

Im still a little confused on how exactly u determine the derivative of an antiderivative. For example if it said

Find the derivative of

d ∫ from x to ln t dt looking at what you did in the last problem would it be ln x?
dx

Please explain.

 

[pka]

If each of H & G is a differentiable function then \(\displaystyle \L
\frac{d}{{dx}}\int_{G(x)}^{H(x)} {f(t)dt} = f(H(x))H'(x) - f(G(X))G'(x).\)