Derivative of a Function - Increment Method Subject: Differential Calculus
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(2+x)²(1-x)³ = uv where
u = (2+x)² and v = (1-x)³
u' = 2(2+x) and v' = -3(1-x)²
The derivative (using the product formula) is
u'v + uv'
= 2(2+x)(1-x)³ + (2+x)²(-3(1-x)²)
Take out the common factor (2+x)(1-x)² to get
(2+x)(1-x)²[2(1-x) - 3(2+x)]
= (2+x)(1-x)²(-4-5x)
= -(2+x)(1-x)²(4+5x)
u = (2+x)² and v = (1-x)³
u' = 2(2+x) and v' = -3(1-x)²
The derivative (using the product formula) is
u'v + uv'
= 2(2+x)(1-x)³ + (2+x)²(-3(1-x)²)
Take out the common factor (2+x)(1-x)² to get
(2+x)(1-x)²[2(1-x) - 3(2+x)]
= (2+x)(1-x)²(-4-5x)
= -(2+x)(1-x)²(4+5x)
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you need the derivative? that would be (2+x)(1-x)^3 + (2+x)^2*-3(1-x)^2
(that's if your original problem was being multiplied together which i think is what you were trying to show)
(that's if your original problem was being multiplied together which i think is what you were trying to show)