power rule

Intro

Differentiating negative power
the power rule also allows us to differentiate expressions like 1/x2

Sample Problem

Find the derivative of f(x)=5/x3-3/x2+8x

Solution

y=5/x3-3/x2+8x
y=5x(-3)-3x(-2)+8x rewrite as power
dy/dx=5.-3.x(-4)-3.-2.x(-3)+8 power rule
=-15x(-4)+6x(-3)+8
=-15/x4+6/x3+8 rewrite as fraction



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