Examples for


Derivatives measure the rate of change along a curve with respect to a given real or complex variable. Wolfram|Alpha is a great resource for determining the differentiability of a function, as well as calculating the derivatives of trigonometric, logarithmic, exponential, polynomial and many other types of mathematical expressions. Differentiation has many applications within physics, trigonometry, analysis, optimization and other fields.


Differentiate an expression with respect to a given variable.

Calculate the derivative of a function:

More examples

Higher-Order Derivatives

Calculate higher-order derivatives.

Compute higher-order derivatives:

More examples

Implicit Differentiation

Differentiate functions implicitly defined by equations.

Differentiate an equation:

Compute a derivative using implicit differentiation:

More examples

Partial Derivatives

Find the partial derivative with respect to a single variable or compute mixed partial derivatives.

Compute partial derivatives:

Compute higher-order partial derivatives:

More examples

Directional Derivatives

Calculate the derivative of a multivariate function in a specified direction.

Compute a directional derivative:

More examples

Derivatives of Abstract Functions

Find the derivative of an arbitrary function.

Compute derivatives involving abstract functions:

Compute partial derivatives of abstract functions:

More examples


Check if functions are differentiable over the field of real numbers.

Test differentiability of a function:

More examples

Derivative Applications

Explore many applications of derivatives.

Find intervals of monotonicity:

Explore notable points of curves:

Compute extreme values of univariate and multivariate functions:

Calculate the tangent line of an equation at a given point:

More examples