When the upper limit of a definite integral is itself a function of x rather than x alone, its derivative is found by combining the Fundamental Theorem of Calculus with the chain rule: differentiating the accumulation function evaluated at the inner function equals the integrand evaluated at that inner function, multiplied by the derivative of the inner function. This is a topic in differential and integral calculus concerning the differentiation of integrals with variable limits, treating the definite integral as a composite function whose "outside" function is the antiderivative given by the Fundamental Theorem of Calculus and whose "inside" function is the variable upper limit.
When the upper limit of a definite integral is itself a function of x rather than x alone, its derivative is found by combining the Fundamental Theorem of Calculus with the chain rule: differentiatin…