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