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Definition of Derivative: More General Definition

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First published at 20:14 UTC on April 7th, 2018.

#mathematics
#calculus
#science

Math Easy Solutions

MES

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In this video I revisit the definition of derivative, and this time look at a more general definition which involves the horizontal axis to be a more general function of x, and not necessarily just x. The derivative is defined as the instantaneous slope tangent to a curve at a specific point. But when the horizontal and vertical axes are both general functions of x, the formulation for the instantaneous slope can still be formulated similar to the simple definition of the derivative. The only difference is that with some simple algebra and limits manipulation, the instantaneous slope can be written as the derivative of the vertical axis function divided by the derivative of horizontal axis function. When the horizontal axis funciton is equal to x, then it's derivative is one, thus the general case simplifies into the basic definition that we accustomed to.

This is a very interesting concept and is neccessary to understand for my next video, which is on visualizing Cauchy's Mean Value Theorem, so make sure to watch this video and stay tuned for my next video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtgGej0EjQ7q-CRyjw

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/definition-of-derivative-more-general-definition

Related Videos:

Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Derivative as a function: Graphing Derivatives: http://youtu.be/9LOLieu4G3I
Limit Laws - Proof of Quotient Law: http://youtu.be/91D_6wru6G4 .

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