Implicit differentiation

Calculus Tutorial

Implicit differentiation

Intro

In implicit differentiation, we differentiate both sides of the equation according to x and treat y as an implicit function of x

Sample Problem

3xy+x2-2y3=7
find dy/dx

Solution

3xy+x2-2y3=7
d/dx(3xy+x2-2y3)=d/dx(7) — differentiate
3.d/dx(xy)+d/dx(x2)-2.d/dx(y3)=d/dx(7)
3(y.1+x.dy/dx)+2x-2.3y2dy/dx=0 — produt rule and power rule
3y+3x.dy/dx+2x-6y2.dy/dx=0 — simplify
(3x+6y2)dy/dx=-3y-2x — simplify
dy/dx=-(2x+3y)/(3x+6y2)



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