Suppose I ~ IR is a closed interval and that f: [a, b] x I ~ JR is such that ai/at
Chapter 10, Problem 12(choose chapter or problem)
Suppose I ~ IR is a closed interval and that f: [a, b] x I ~ JR is such that ai/at existson [a, b] x I, and for each t E [a, b] the function x 1-+f(t, x) is in n*(/) and thereexist a, wE n*(/) such that the partial derivative satisfies a(x) ~ of(t, x)lot ~ w(x) for a.e.x E I. If F(t):= JI i(t,x)dx, show that F is differentiable on [a,b] and that F'(t):=JI oi(t, x)/ot dx.
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