Partial Derivative Calculator

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Introduction to Partial Derivative Calculator

Partial derivative calculator with steps finds the derivative of a curve with numerous variables online. This partial derivatives calculator has the ability to differentiate a function numerous times.

Measuring the rate of change of the function with regard to one variable is known as partial derivatives in mathematics. It handles variables like x and y, functions like f(x), and the modifications in the variables x and y.

With partial derivatives calculator, you can learn about chain rule partial derivatives and even more. To easily obtain the derivatives, partial differentiation calculator can be used free online.

Related: You can also find implicit differentiation calculator and second order derivative calculator to further consolidate your concepts regarding derivatives and its calculations.

Process of using Second Order Partial Derivative Calculator

Partial differentiation calculator takes the partial derivative of a function by dividing the function into parts. Below is the process of using partial differentiation calculator with steps.

How to give input:

  • First, write a differentiation function or pick from examples.
  • Now, from the drop-down list, choose the derivative variable.
  • Next, decide how many times the given function needs to be differentiated.
  • Press the calculate button to see the results.

The second partial derivative calculator will instantly show you step by step results and other useful metrics.

You can also find directional derivative calculator for the calculations of directional derivatives.

How Partial Differentiation Calculator shows output?

The first partial derivative calculator uses derivative rules and formulas to evaluate the partial derivative of that function.

In results, it shows you derivative (for calculating derivative of a function only, use derivative function calculator on home page. Apart from that second partial derivative calculator shows you possible intermediate steps, 3D plots, alternate forms, rules, series expension and the indefinite integral as well. You can also use indefinite integral with steps for more learning and practice.

Formulas used by Partial Derivative Calculator

The partial derivative of the function f(x,y) partially depends upon "x" and "y". So the formula for for partial derivative of function f(x,y) with respect to x is:

$$ \frac{∂f}{∂x} = \frac{∂f}{∂u}\frac{∂u}{∂x} \;+\; \frac{∂f}{∂v}\frac{∂v}{∂x} $$

Simiarly, partial derivative of function f(x,y) with respect to y is:

$$ \frac{∂f}{∂y} = \frac{∂f}{∂u}\frac{∂u}{∂y} \;+\; \frac{∂f}{∂v}\frac{∂v}{∂y} $$

Related: Also use other useful tools on this website like we offer third derivative calculator with steps for you to calculate higher order derivatives easily online.

Solved example of Partial Differentiation Calculator

Suppose we have to find partial derivative of Sin(x4)

By putting values in calculator, we got solution:

$$ \frac{d}{dx} sin(x^4) \;=\; 4x^3 cos(x^4) $$


Partial differentiation calculator is an web based tool which work with mathematical functions along with multiple variables. Because of this, it becomes easy to solve and evaluate partial differentiation functions. The partial differentiation solver shows you different metrics and details which are essential for you to learn this concept.

Related: On this website, you can also find local linearization calculator for finding linear approximation.

Besides this, learn different ways to find derivative of a function from these guides.

What are the benefits of using first partial derivative calculator?

One of the major advantages of this calculator is accuracy. If you find derivatives manually, it is possible that you may get stuck in the middle of a maths problem and won’t get rid of it for an hour. If you use a partial derivative tool it provides you an accurate result in a single click.

What is the chain rule in differential equations?

According to the chain rule, the derivative f (g (x)) equals f'(g (x)) g' (x). Partial derivatives Calculator uses the chain rule to differentiate composite functions.

Also find multivariable chain rule calculator on this website to find the derivative of the composition of two differentiable functions.

Why is the partial derivative test of second order useful?

You could use second-order partial derivatives to identify whether the location is local maxima, minimum, or a saddle point. Once you've found the zero vector slope of the multivariate function, it indicates the tangent plane of the graph is smooth at that point.

We hope you find above calculator helpful regarding your calculations. There are other related tools just like product rule solver and derivative quotient calculator which you can use for more practice and learning.

Frequently Asked Questions

Is partial differential equations hard?

Yes, the partial differential equations are hard to solve. But when these equations are converted into ordinary differential equations, we can evaluate them with different methods or by using partial differential calculator.

What is the difference between ordinary differential equations and partial differential equations?

The ordinary differential equations (ODEs) are those equations where the derivatives are taken with respect to one independent variable. Whereas the partial differential equations (PDE’s) are those equations where the derivatives are taken with respect to more than one variables.

What is first order partial derivatives?

The derivative of a multivariable function with respect to an independent variable one time, is known as first order partial derivative. In partial derivative, we differentiate a function with one variable by treating other as a constant. We can use first order partial derivatives calculator to solve them online.

What is continuous first order partial derivatives?

The partial derivative of a continuous function is known as continuous partial derivative if the derivative is also continuous. But for a continuous function, it is not necessary that its derivative should also be continuous.

What is elliptic partial differential equations?

A second order partial differential equation (PDE)

Auxx+2Buxy+Cuyy+Dux+Fuy+G=0 is considered as elliptic if, B2−AC < 0. Elliptic partial differential equations have no real characteristic surfaces.

You can use partial differential equations calculator above to solve your equations online.

What is the chain rule of partial differentiation?

The chain rule partial differentiation is a technique in which we differentiate a function with respect to two or three variables at a time.

For a function f=f(u,v), u=u(x,y) and v=v(x,y) the chain rule is,

$$ \frac{df}{dx} \;=\; \frac{df}{du}\frac{du}{dx} \;+\; \frac{df}{dv}\frac{dv}{dx} $$


$$ \frac{df}{dy} \;=\; \frac{df}{du}\frac{du}{dy} \;+\; \frac{df}{dv}\frac{dv}{dy} $$

Use chain rule partial derivative calculator to differentiate chain rule partial differentiation online step by step.

Alan Walker

Alan Walker

Last Updated November 21, 2022

I am Mathematician, Tech geek and a content writer. I love solving patterns of different math queries and write in a way that anyone can understand. Math and Technology has done its part and now its the time for us to get benefits from it.