Calculus practice problems

Limits, derivatives, integrals, series and multivariable ideas, with verified step-by-step work. Each problem below has a full solution whose steps and answer come from the exact math engine.

Derivatives

Power, product, quotient and chain rules.

Easy

Find

\frac{d}{dx}\left(x^3\right)

A direct application of the power rule.

Medium

Find the derivative of

x^2 \sin x

A product of two functions needs the product rule.

Easy

Differentiate

e^{3x}

The chain rule with a linear inner function.

Medium

Differentiate

\ln(x^2 + 1)

Chain rule with the natural logarithm.

Practise with: Derivative Calculator, Implicit Differentiation Calculator

Integrals

Antiderivatives, substitution and the Fundamental Theorem.

Easy

Evaluate

\int_0^1 x^2\,dx

The Fundamental Theorem with the power rule for antiderivatives.

Easy

Evaluate

\int_1^3 2x\,dx

Antiderivative x squared, evaluated at the bounds.

Easy

Find

\int \cos x\,dx

A basic trigonometric antiderivative; do not forget the constant.

Easy

Evaluate

\int_0^4 x\,dx

The area of a triangle with base 4 and height 4.

Practise with: Integral Calculator, Definite Integral Calculator

More practice

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