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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d y}{d t} = y \cdot ln (t), y (e) = 200

x \to 2 lim (\frac{- x}{( 2 - x )})

\int e^{x + 7 e^{x}} d x

\frac{d}{d x} (3 x^{2} - 4)

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

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