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