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Polynomials: Differentiation Rules
Without expanding the brackets, use the Product Rule to differentiate:
( w2 + 6 w + 4 )( 2 w + 5 )
The derivative is: w4 + w3 + w2 + w +

tickcross


Worked Solution:

The Product Rule:
If y = u v where u and v are functions of w then
dy
---
dw
 = v
du
---
dw
 + u
dv
---
dw
Here, u = w2 + 6 w + 4 and v = 2 w + 5
=>
du
---
dw
 = 2 w + 6 and
dv
---
dw
 = 2
The derivative of the product is ( 2 w + 5 )( 2 w + 6 ) + ( w2 + 6 w + 4 )( 2 )
= 6 w2 + 34 w + 38

© MEI Produced by Dr Ron Knott, revised 15 May 2007
tom . button [AT] mei . org . uk 		Test reference: PolyDiffRules.html?ref=4090,qu=prod