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

The derivative of (x^2+3x+5)/(x^2-1) is (-3x^2-12x-3)/((x^2-1)^2)

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

The first derivative of (x^2+3x+5)/(x^2-1) is (-3x^2-12x-3)/((x^2-1)^2)

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derivative of

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

\frac{- 3 x ^{2} - 12 x - 3}{( x ^{2} - 1 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(2 x + 3) (x^{2} - 1) - 2 x (x^{2} + 3 x + 5) : - 3 x^{2} - 12 x - 3

= \frac{- 3 x ^{2} - 12 x - 3}{( x ^{2} - 1 ) ^{2}}

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

\frac{d}{d x} (3 x^{4} y^{5} + 5 x^{4} y^{3})

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

2 a^{x}

(4 x^{5} + 1)^{3}

What is the derivative of (x^2+3x+5)/(x^2-1) ?
The derivative of (x^2+3x+5)/(x^2-1) is (-3x^2-12x-3)/((x^2-1)^2)
What is the first derivative of (x^2+3x+5)/(x^2-1) ?
The first derivative of (x^2+3x+5)/(x^2-1) is (-3x^2-12x-3)/((x^2-1)^2)