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Implicit Differentiation Calculator

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

About Implicit Differentiation Calculator

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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