Implicit Differentiation

This calculus video tutorial provides a basic introduction into implicit differentiation. it explains how to find dy/dx and evaluate it at a point. It also explains how to find the slope of a curve given the x and y coordinates. In addition, it explains how to find d^2y/dx^2, the second derivative of the function using implicit differentiation. You need to be familiar with the product rule, chain rule, and quotient rule for derivatives.

Derivatives - The Product Rule - f*g:

Derivatives - The Quotient Rule:

Derivatives - The Chain Rule:

Derivatives - Composite Functions:

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Implicit Differentiation:

Derivatives of Inverse Trig Functions:

Derivatives of Exponential Functions:

Derivatives of Logarithmic Functions:

Logarithmic Differentiation:

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Derivatives - Using Logarithms:

Derivatives of Inverse Functions:

Derivatives - Differentiation Rules:

Derivatives - Function Notations:

Derivatives - The Reciprocal Rule:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

Derivatives - Formula Sheet:

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[dong-wooklee]

Shortcut for implicit differentiation
Take all the things on one side
then do as below:
dy/dx= -(diffentiate wrt x, take y as a constant)/(differentiate wrt y, take x as a constant)

Eg. Lets say I need to differentiate x³+3xy=y²+1

Step1
(taking everything on one side)
x³+3xy-y²-1=0

Step2
differentiate x³+3xy-y²-1 wrt x and take y as a constant
That would be equal to 3x²+3y
Let 3x²+3y = m

Step3
differentiate x³+3xy-y²-1 wrt y and take x as a constant
That would be equal to 3x-2y
Let 3x -2y = n

Step4
Apply the rule and obtain dy/dx
dy/dx = -m/n = -3x²-3y/3x-2y

This may look like this is quite lengthy but in actual it hardly takes 10secs. I wrote this long so that anyone who sees this could clearly make sense of it and understand

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