M Marierose New member Joined Feb 15, 2006 Messages 10 Feb 21, 2006 #1 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.
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 Elite Member Joined Jan 29, 2005 Messages 11,978 Feb 22, 2006 #2 If each of H & G is a differentiable function then \(\displaystyle \L \frac{d}{{dx}}\int_{G(x)}^{H(x)} {f(t)dt} = f(H(x))H'(x) - f(G(X))G'(x).\)
If each of H & G is a differentiable function then \(\displaystyle \L \frac{d}{{dx}}\int_{G(x)}^{H(x)} {f(t)dt} = f(H(x))H'(x) - f(G(X))G'(x).\)
