## 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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