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