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# 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:

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Higher-Order Derivatives

Calculate higher-order derivatives.

Compute higher-order derivatives:

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Implicit Differentiation

Differentiate functions implicitly defined by equations.

Differentiate an equation:

Compute a derivative using implicit differentiation:

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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:

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Directional Derivatives

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

Compute a directional derivative:

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Derivatives of Abstract Functions

Find the derivative of an arbitrary function.

Compute derivatives involving abstract functions:

Compute partial derivatives of abstract functions:

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Differentiability

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

Test differentiability of a function:

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