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Popular >

derivative of ((3x-1)/(2x+1))

Solution

\frac{d}{d x} (\frac{( 3 x - 1 )}{2 x + 1})

Solution

\frac{5}{( 2 x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 3 x - 1 )}{2 x + 1})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 3 x - 1 ) ( 2 x + 1 ) - \frac{d}{d x} ( 2 x + 1 ) ( 3 x - 1 )}{( 2 x + 1 ) ^{2}}

\frac{d}{d x} (3 x - 1) = 3

\frac{d}{d x} (2 x + 1) = 2

= \frac{3 ( 2 x + 1 ) - 2 ( 3 x - 1 )}{( 2 x + 1 ) ^{2}}

Expand

3 (2 x + 1) - 2 (3 x - 1) : 5

= \frac{5}{( 2 x + 1 ) ^{2}}

Popular Examples

integral of 4cos(sqrt(x))

\int 4 cos (x) d x

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f (x) = x^{\frac{3}{2}} + \frac{1}{x ^{\frac{5}{2}}}

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\frac{d}{d x} (x^{2} e^{7 x})

integral of ((e^t+2e^{2t}))/(e^{3t)}

\int \frac{( e ^{t} + 2 e ^{2 t} )}{e ^{3 t}} d t

(\partial)/(\partial x)(u/x)

\frac{\partial}{\partial x} (\frac{u}{x})

Frequently Asked Questions (FAQ)

What is the derivative of ((3x-1)/(2x+1)) ?
The derivative of ((3x-1)/(2x+1)) is 5/((2x+1)^2)
What is the first derivative of ((3x-1)/(2x+1)) ?
The first derivative of ((3x-1)/(2x+1)) is 5/((2x+1)^2)