g(x)=(x-1)²√1+2x)maka g'(x)=
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g(x)=(x-1)²√1+2x)maka g'(x)=
1 Jawaban
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1. Jawaban Anonyme
y = uv
y' = u'v + uv'
g(x) = (x - 1)² √(1 + 2x)
g'(x) = 2 (x - 1) √(1 + 2x) + (x - 1)² [1/2 (1 + 2x)^(-1/2) (2)]
= 2 (x - 1) √(1 + 2x) + (x - 1)² [1 / √(1 + 2x)]
= [2 (x - 1)(2x + 1) + (x - 1)²] / √(1 + 2x)
= [2 (2x² + x - 2x - 1) + (x² - 2x + 1)] / √(1 + 2x)
= (5x² - 4x - 1) / √(1 + 2x)
= (x - 1)(5x + 1) / √(1 + 2x)