Partial Derivative Calculator

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This is a partial derivative calculator.

A partial derivative is a derivative taken of a function with respect to a specific variable.

The function is a multivariate function, which normally contains 2 variables, x and y. However, the function may contain more than 2 variables.

So when we take the partial derivative of a function, we take it with respect to a specific variable.

As an example, let's say we want to take the partial derivative of the function, f(x)= x³y², with respect to x.

So since we are finding the derivative with respect to x, we find the derivative of the x component of the function. Since x is raised to the power of 3, the derivative of the x component is 3x². This is gotten simply by using the power rule in calculus.

Since we are not taking the derivative of the function with respect to y, we leave the y component unchanged.

Thus, the complete partial derivative of the function, x³y², with respect to x, is 3x²y²

Now let's do the same function but now find the partial derivative of it with respect to y.

So, again, the original function is, f(x)= x³y²

Now we are simply going to find the partial derivative with respect to y.

So, again, using the power rule in calculus, we can find the derivative of the y component of the function. Doing so gives us, 2y.

The x component of the function is unchanged, because we are not finding the derivative of the function with respect to x.

Thus, the partial derivative of the function, x³y², with respect to y, is 2x³y

Partial differentiation is important when you want to see how the rate of change of one variable affects a function that has multiple variables. By taking the partial derivative of a function, we can see how the rate of change of that one variable affects the entire function.

Normally, partial differentiation is done on functions that contain 2 variables, but some functions may have more.

From a technical perspective, for those who want to know the technical aspect of it, this calculator is built using the sympy module in the Python programming language.

This calculator can take the partial derivative of regular functions, as well as trigonometric functions.

This user simply enters in the function and the variable to differentiate with respect to. The resultant partial derivative will then be automatically computed and displayed.

Related Resources

Second Order Partial Derivative Calculator

Higher Order Partial Derivative Calculator