50 Challenging Calculus Problems (Fully Solved)

These 50 challenging calculus problems involve applying a variety of calculus skills. The exercises come with a good range of difficulty from milder challenges to very hard problems. On the page following each problem you can find the full solution with explanations.

derivatives of polynomials, trig functions, exponentials, and logarithms
the chain rule, product rule, and quotient rule
second derivatives (and beyond)
applications such as related rates, extreme values, and optimization
limits, including l’Hopital’s rule
antiderivatives of polynomials, trig functions, exponentials, and logarithms
definite and indefinite integrals
techniques of integration, including substitution, trig sub, and integration by parts
multiple integrals
non-Cartesian coordinate systems