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

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

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

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

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

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

Solution steps

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

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

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

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

Expand

2 (x^{2} - 1) - 2 x (2 x + 1) : - 2 x^{2} - 2 x - 2

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

\frac{d}{d t} (\frac{( t ^{3} - 6 t ^{2} + 7 )}{( 2 t ^{2} + 6 t )})

e^{3 x + 2} + 5

(((e^{e})^{e})^{x})^{2}

5 x^{3} + 16 b^{2}

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

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