Implicit Differentiation - How it's done

Implicit Differentiation - How it's done

Given an equation relating y and x, see how y' is determined using implicit differentiation. Experienced and prospective Mathematica users: See note below.

  1. Here is the equation you submitted:
  2. Differentiate both sides of the equation with respect to x and get _
  3. You now solve for y' in terms of x and y.
    Multiple values for y'[x]: Created by webMathematica
The expression for y' can often be simplified.

Ken Levasseur
Mathematical Sciences
UMass Lowell
Ken's WebMathematica Scripts

Input for this script is the conventional way that an implicit relationship beween x and y is expressed in calculus textbooks. In Mathematica you need to make this relationship explicit by using y[x] in place of y. This is done automatically in the script by replacing all occurances of y with y[x]. back to the top of the page

Script generated by MSPWizard.nb