Chain Rule with FTC

Calculus 1 · Axiom Academy

Differentiate an integral with a variable upper limit using FTC Part 1 and the Chain Rule. Find the derivative . The upper limit is x^2 , not just x , so a plain application of FTC Part 1 won't be enough. Nice work — you combined FTC Part 1 with the Chain Rule to differentiate an integral whose upper limit is itself a function. FTC Part 1: — differentiating undoes integrating. Chain rule extension: when the upper limit is g(x) , evaluate the integrand at g(x) and multiply by g'(x) . The same recipe handles any function defined by an integral with a variable upper limit.

This is the written version of the interactive lesson above. See the full Calculus 1 course.