implicit differentiation

Calculus Tutorial

implicit differentiation

Intro

Evaluating derivative with implicit differentiation.

Sample Problem

Find the slope of the tangent line to the curve x3+(y-x)2=5 at(1,3).

Solution

x3+(y-x)2=5
d/dx((x3)+(y-x)2)=d/dx(5)
d/dx(x3)+d/dx(y-x)2=0
3×2+2(y-x)(dy/dx-1)=0 differentiative
3×2+2(y-x)dy/dx-2(y-x)=0 simplify
2(y-x)dy/dx=2(y-x)-3×2
dy/dx=(2(y-x)-3×2)/2(y-x)
dy/dx=(2(3-1)-3.1)/2(3-1) substitute x=1,y=3
=(2.2-3)/2.2
=1/4
slope of tangent=1/4



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