Examples for

# Derivatives

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.

### Derivatives

Differentiate an expression with respect to a given variable.

#### Calculate the derivative of a function:

### Implicit Differentiation

Differentiate functions implicitly defined by equations.

#### Differentiate an equation:

#### Compute a derivative using implicit differentiation:

### Derivatives of Abstract Functions

Find the derivative of an arbitrary function.

#### Compute derivatives involving abstract functions:

#### Compute partial derivatives of abstract functions:

### Higher-Order Derivatives

Calculate higher-order derivatives.

#### Compute higher-order derivatives:

### 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:

### Differentiability

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

#### Test differentiability of a function:

### GO FURTHER

Step-by-Step Solutions for DerivativesCalculus Web AppFree Unlimited Calculus Practice Problems### RELATED EXAMPLES

### Directional Derivatives

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

#### Compute a directional derivative:

### Derivative Applications

Explore many applications of derivatives.