# Implicit Differentiation Calculator

Implicit Differentiation calculator is a free online calculator that displays the derivative of the given function with respect to the variable.

### Inputs

1. Implicit form function

### Steps To Use Calculators

The following steps show how to use the implicit Differentiation calculator

1. Type the equation into the appropriate input field.
2. To receive the derivative of a function, click the “Submit” button.
3. In the new window, the derivative will be displayed.

### Outputs

1. Input Interpretation
2. Results

## Implicit Differentiation

In Calculus, a function can be in implicit form at times and it signifies that the function is expressed in both x and y terms. The implicit form of a parabola equation for example is $$y2 = – 4ax$$. The process of determining the derivative of these implicit functions is called implicit differentiation.

## Steps

• Firstly, you need to differentiate the function with respect to x.
• While differentiating y terms you get dy/dx.
• Then, collect all dy/dx on one side.
• Lastly, solve for dy/dx.

## Example Problems

Question 1: Find y′ for xy=1?

Solution: Given implicit function => xy =1

Differentiating with respect to x.

=> d(xy)/dx = d(1)/dx

Using product rule, we differentiate the first term

=> 1.y + x.(dy/dx) = 0

We know that y′ = dy/dx

y + xy′ = 0

=> y′ = -y/x

From the equation we know that y = 1/x, substituting this in the implicit differential, we get

=> y′ = 1/x2

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