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Implicit Differentiation Calculator

# Implicit Differentiation Calculator

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Differentiation is the process of finding the rate at which one variable changes with respect to the other. Implicit differentiation is a process of finding derivative of a function without separating the variables. Implicit differentiation calculator is the online tool which can easily give the derivative value of any function using this method.

Example 1: Find the implicit derivative of the function, 3x2 – y3= 4

Given function: 3x2 – y3 = 4

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

6x – 3y2 (dy/dx) = 0  -> Derivative of a constant is ‘0’.

Now solve for ‘dy/dx’

-3y2(dy/dx) = -6x

dy/dx = -6x/-3y2 -> dy/dx = 2x/y2

Example 2:  Find the implicit derivative of the function, y3 + 2x= 1

Given function: y3 + 2x= 1

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

3y2 (dy/dx) + 2 = 0 -> Derivative of a constant is ‘0’

Now solve for ‘dy/dx’

3y2(dy/dx) = -2

dy/dx = -2/3y2