Basic Analysis I — Real Analysis · Problem 5.3.2

This is a chain rule problem disguised as calculus. The Fundamental Theorem of Calculus tells you that differentiating an integral with respect to its upper limit gives you the integrand evaluated there—but here the upper limit isn't just $x$, it's $x^2$. So you need to multiply by the derivative of that upper limit using the chain rule: the derivative of $x^2$ is $2x$.

This is a chain rule problem disguised as calculus. The Fundamental Theorem of Calculus tells you that differentiating an integral with respect to its upper limit gives you the integrand evaluated there—but here the upper limit isn't just $x$, it's $x^2$. So you need to multiply by the derivative of that upper limit using the chain rule: the derivative of $x^2$ is $2x$.