Differentiate rational functions

Calculus Tutorial

Differentiate rational functions

Intro

d/dx(xn)=nx(n-1)
d/dx(x)=1
d/dx(c)=0

Sample Problem

what is the value of d/dx((3x+2)/(2×2-1)) at x=1

Solution

y=(3x+2)/(2×2-1)
dy/dx=((2×2-1).d/dx(3x+2)-(3x+2).d/dx(2×2-1))/(2×2-1)2 — quotient rule
=((2×2-1).3-(3x+2).4x)/(2×2-1)2 —power rule
=(6×2-3-12×2-8x)/(2×2-1)2 — expand
=(-6×2-8x-3)/(2×2-1)2 — simplify
=(-6.1-8.1-3)/(2.1-1) — substituting x=1
=-17/1
=-17



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