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Polynomials: Differentiation Rules
Without expanding the brackets, use the Product Rule to differentiate:
( x2 + 2 x – 1 )( 4 x – 6 )
The derivative is: x4 + x3 + x2 + x +

tickcross


Worked Solution:

The Product Rule:
If y = u v where u and v are functions of x then
dy
---
dx
 = v
du
---
dx
 + u
dv
---
dx
Here, u = x2 + 2 x – 1 and v = 4 x – 6
=>
du
---
dx
 = 2 x + 2 and
dv
---
dx
 = 4
The derivative of the product is ( 4 x – 6 )( 2 x + 2 ) + ( x2 + 2 x – 1 )( 4 )
= 12 x2 + 4 x – 16

© MEI Produced by Dr Ron Knott, revised 15 May 2007
tom . button [AT] mei . org . uk 		Test reference: PolyDiffRules.html?ref=35006