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Sidana [21]
3 years ago
6

Y=(3x-2)/(sqrt(2x+1)) differentiate

Mathematics
1 answer:
Mumz [18]3 years ago
8 0
y=\dfrac{3x-2}{\sqrt{2x+1}}=\dfrac{3x-2}{(2x+1)^{1/2}}

The quotient rule gives

y'=\dfrac{(2x+1)^{1/2}(3x-2)'-(3x-2)\left((2x+1)^{1/2}\right)'}{\left((2x+1)^{1/2}\right)^2}=\dfrac{3(2x+1)^{1/2}-\dfrac{2(3x-2)}{2(2x+1)^{1/2}}}{2x+1}

Factor out (2x+1)^{-1/2} to get

\dfrac{(2x+1)^{-1/2}\left(3(2x+1)^{2/2}-(3x-2)\right)}{2x+1}=\dfrac{6x+3-6x+2}{(2x+1)^{3/2}}=\dfrac{3x+5}{(2x+1)^{3/2}}
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