Asked by Amy
Find derivative of the function:
y = (4x+1)^2 (1-x)^3
y = (4x+1)^2 (1-x)^3
Answers
Answered by
oobleck
use the product rule and the chain rule:
y = u^2 v^3
y' = 2u u' * v^3 + u^2 + 3v^2 v'
= uv^2 (2vu' + 3uv')
= (4x+1)(1-x)^2 (2(1-x)(4) + 3(4x+1)(-1))
= 5(4x+1)(1-x)^2 (1-4x)
= -5(16x^2-1)(1-x)^2
y = u^2 v^3
y' = 2u u' * v^3 + u^2 + 3v^2 v'
= uv^2 (2vu' + 3uv')
= (4x+1)(1-x)^2 (2(1-x)(4) + 3(4x+1)(-1))
= 5(4x+1)(1-x)^2 (1-4x)
= -5(16x^2-1)(1-x)^2
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