Derivatives

Find the derivative using the product rule, chain rule and other methods:

derivative of x^4 + 9x^3 + 7x – 2

slope of log(x) / (x^2 + 1)

Integrals

Calculate an integral by substitution, integration by parts and other methods:

integrate sin(x)cos(x)^2

integral of sqrt(a^2 – x^2)

show the integration: arcsec(sqrt(t))

Limits

Learn how to take a limit:

limit of (x – 3) / (x^2 – 2x – 3) as x approaches 3

take the limit as x goes to infinity: (1 + 1/x)^x

Optimization

Find local and global extrema using a variety of tests:

local extrema of x^3 - 3x + 1

find the extrema of 3x^4 - 4x^3 - 12x^2 + 1

maximize sin(x)

Discontinuities

Get hints for discontinuities:

where is (x^2 - 4)/(x^2 - 2x - 3) discontinuous?

discontinuities of sin((x^2-x)/(x-1)) + log(sqrt(abs(x)))