find dy of y = (x) / (√(9x + 4))?
y = (x) / (√(9x + 4))
what the step by step process to the the answer?
answer: (9x + 8) / (2(9x + 4) ^ (3/2) )
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y = (x) / (√(9x + 4))
what the step by step process to the the answer?
answer: (9x + 8) / (2(9x + 4) ^ (3/2) )
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Verified answer
y'={(1)(9x+4)^(1/2)-[9/2(9x+4)^(1/2)](x)}/(9x+4)
[2(9x+4)-9x]/2(9x+4)^(1/2)]/(9x+4)
(9x+8)/2[(9x+4)^(3/2)]
Quotient Rule:
[sqrt(9x+4) * 1 - x * 9/2*sqrt(9x+4)^(-1/2)] / (9x+4)
From here it's just algebra.
y' = -9x/2*(9x + 4)^(-1/2) + 1/â(9x + 4)
y' = (1 - 9x/2)/(â(9x + 4))
y = (x) / (â(9x + 4))
dy= [(â(9x + 4))*1 + x*{1/2â(9x + 4}*9x]/(9x + 4)
=[(9x+4)+4.5x^2]/(9x + 4) ^ (3/2)