Partial Derivative Calculator
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Partial Derivative Examples
About Partial Derivative Calculator
A free partial derivative calculator that calculates the partial derivatives of a function and displays the step-by-step solution. For example, for f(x,y)=x^2y+3y, the partial derivative with respect to x is 2xy, and the partial derivative with respect to y is x^2+3.
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Frequently Asked Questions
How to use the partial derivative calculator
Enter a function with two or more independent variables, such as f(x,y)=x^2y+3y. Click "Solve" to view the partial derivatives for each variable.
What is a partial derivative
A partial derivative is the derivative of a multivariable function, obtained by differentiating only one independent variable while keeping other variables constant. It describes the rate of change of the function along a specific coordinate axis. Partial derivatives are usually represented by the symbol ∂.
What is the difference between a partial derivative and a regular derivative
The core difference between a derivative and a partial derivative lies in the number of independent variables of the function. Ordinary derivatives are typically used for functions with a single variable, while partial derivatives are used for functions with multiple variables. Partial derivatives require specifying which variable to differentiate from. For example, the partial derivative of f(x,y)=xy with respect to x is y, and the partial derivative with respect to y is x.
How are other variables treated when taking partial derivatives
They are treated as constants. For example, when taking the partial derivative of (f(x,y)=x^2y) with respect to (x), (y) is treated as a constant, resulting in (2xy).
Can the same function have different partial derivatives
Yes. A multivariate function has multiple independent variables, and partial derivatives can be taken with respect to each variable. Therefore, a function usually has several partial derivatives (e.g., partial derivative with respect to x, partial derivative with respect to y), but they correspond to rates of change in different directions.
What does a partial derivative of 0 mean
A partial derivative of 0 means that the rate of change of the function along the direction of the corresponding variable at that point is zero.
