Negative power differentiation

Calculus Tutorial

Negative power differentiation

Intro

We can rewrite each rational term in the expression as a negative power of x

Sample Problem

y=3/x2-2/x3
find dy/dx at x=-1

Solution

y=3/x2-2/x3
dy/dx=d/dx(3/x2-2/x3)
dy/dx=d/dx(3/x2)-d/dx(2/x3)
dy/dx=3.d/dx(x(-2))-2.d/dx(x(-3))
dy/dx=3(-2.x(-3))-2(-3.x(-4))
dy/dx=-6.1/x3 +6/x4
dy/dx=-6/x3+6/x4
dy/dx(at x=-1)=-6/(-1)3+6/(-1)4
=-6/-1+6/1
=6+6
=12



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