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FTC Part 1 — Derivative of an Integral with Variable Upper Bound

d/dx[∫[a,x] f(t) dt] = f(x). Chain rule version: d/dx[∫[a,g(x)] f(t) dt] = f(g(x))·g'(x).

CalculusCommon Core FUN-5.CFUNVerified correct ✓

Worked examples

Find d/dx[∫[0,2x³] cos(t) dt] using FTC Part 1 and the chain rule.
Answer: 6*x**2*cos(2*x**3)
Find d/dx[∫[0,x²] cos(t) dt] using FTC Part 1 and the chain rule.
Answer: 2*x*cos(x**2)

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