Examples for

Step-by-Step Calculus


Explore the steps for derivative calculations using the power rule:

Find the derivative using the product rule:

Compute derivatives using the quotient rule:

See step by step how to apply the chain rule:

Use the limit definition to compute derivatives:

Find partial derivatives of multivariate expressions:

See how to evaluate derivatives at a given point:

Perform logarithmic differentiation to compute a derivative:


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

Use u-substitution to compute an integral step by step:

Compute an integral by parts:

Integrate using trigonometric substitution:

See the steps for definite integration over an interval:

See the steps for multivariate integration over a given domain:

Tangent Lines & Planes

Find a line tangent to a curve using the derivative at a point:

Calculate a multivariate tangent plane by examining partial derivatives:

Area between Curves

Learn how to compute the area between curves:

Vector Analysis

See the steps to compute the gradient:

Learn how to compute the divergence:

Calculate the curl:

Applications of Derivatives

Find the line tangent to a curve at a point step by step:

Compute the local maxima or minima of a function:

Show the steps for finding the global minima or maxima of a function:

Discover how to calculate the extrema of a function on a given interval:

Find the inflection points of a function:


Learn how to take a limit:

Calculate a limit approaching infinity:

Perform a one-sided limit step by step:

Use L'Hôpital's rule to compute a limit:

See the steps to use the squeeze theorem on a limit:


Get step-by-step solutions for finding discontinuities:

Arc Length

Calculate the arc length of a curve step by step:

Specify a curve in polar coordinates:

Specify a curve parametrically:

Sum Convergence

Learn how to compute the convergence of an infinite sum:

Determine whether a series converges step by step:

Test whether a series converges absolutely:

Explore divergent series:


  • Arc Length
  • Area between Curves
  • Continuity
  • Derivatives
  • Inflection Points
  • Integrals
  • Limits
  • Optimization
  • Optimization

    Explore step by step a variety of tests to discover local and global extrema:

    Inflection Points

    Calculate inflection points step by step:

    Applications of Integration

    Find the average value of an equation on an interval:

    Look through the steps to find the average value of a derivative on an interval:

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