Implicit Derivative Calculator

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Implicit derivative is a method of finding the derivative of a function, without solving for ‘y’ directly. If ‘y’ is

written as an implicit function with ‘x’, then in this method derivative for each term is taken directly. Implicit

derivative calculator is the simple online tool which can easily find the implicit derivative of any given function.


Example 1: Find the implicit derivative of the function, x2 – y2 = 15

Given function: x2 – y2 = 15

Now to find the implicit derivative, without solving for ‘y’ we start finding the derivative of each term of the

function.

Power rule of the Derivatives    d f(xn)/dx = n*xn-1

Applying the above formula to the given function, we get

2x – 2y (dy/dx) = 0 - Derivative of a constant is ‘0’.

Now solve for ‘dy/dx’

-2y(dy/dx) = -2x

dy/dx = x/y



Example 2: Find the implicit derivative of the function, y4 + x3 = 6

Given function: y4 + x3 = 6

Now to find the implicit derivative, without solving for ‘y’ we start finding the derivative of each term of the

function.

Power rule of the Derivatives  d f(xn)/dx = n*xn-1

Applying the above formula to the given function, we get

4y3(dy/dx) + 3x2 = 0  ->  Derivative of a constant is ‘0’.

Now solve for ‘dy/dx’

4y3(dy/dx) = -3x2

dy/dx = -3x2/ 4y3

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