What is the derivative of (2x+1/(3x-1)) ?

The derivative of (2x+1/(3x-1)) is -5/((3x-1)^2)

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

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

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

- \frac{5}{( 3 x - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( 3 x - 1 ) - 3 ( 2 x + 1 )}{( 3 x - 1 ) ^{2}} : - \frac{5}{( 3 x - 1 ) ^{2}}

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

\int (x - 1) (x + 2) (x + 4) d x

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

y y^{^{'}} = (y^{2} - y) (2 x + 5)

\int sin (3 x) - cos (3 x) d x

y^{^{''}} + 4 y^{^{'}} + 5 y = 10

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