if F(x)=f(g(x)), where g(2)=4, g'(2)=3, and f'(4)=5, find F'(2)

Use the chain rule for the derivative of a function of a function

F'(x) = df/dg * dg/dx
where df/dg is at g = 4 and equals 5
and dg/dx is at x = 2 and equals 3

Thus F'(2) = 5*3 = 15