We know that f(x)= x^2 ∫g(t)dt 0 What is f'(x) and which conditions are necessary for g(t)?
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Originally Posted by antero We know that f(x)= x^2 ∫g(t)dt 0 What is f'(x) and which conditions are necessary for g(t)? Let . Then . From the chain rule: .
Originally Posted by antero We know that f(x)= x^2 ∫g(t)dt 0 What is f'(x) and which conditions are necessary for g(t)? By the "Fundamental theorem of Calculus", the derivative of , with respect to u, is g(u). Here, so, by the chain rule, . The only "conditions" on g are that it be continuous.
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