What is the derivative of (4x-7)/(x^2-1) ?

The derivative of (4x-7)/(x^2-1) is (-4x^2+14x-4)/((x^2-1)^2)

What is the first derivative of (4x-7)/(x^2-1) ?

The first derivative of (4x-7)/(x^2-1) is (-4x^2+14x-4)/((x^2-1)^2)

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derivative of

\frac{4 x - 7}{x ^{2} - 1}

\frac{- 4 x ^{2} + 14 x - 4}{( x ^{2} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 7}{x ^{2} - 1})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x - 7 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 4 x - 7 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (4 x - 7) = 4

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

= \frac{4 ( x ^{2} - 1 ) - 2 x ( 4 x - 7 )}{( x ^{2} - 1 ) ^{2}}

Expand

4 (x^{2} - 1) - 2 x (4 x - 7) : - 4 x^{2} + 14 x - 4

= \frac{- 4 x ^{2} + 14 x - 4}{( x ^{2} - 1 ) ^{2}}

\int 2 x + 1 - 2 d x

\int \frac{x}{x - 11} d x

x^{3} + y^{3} = 3 x y^{2} \frac{d y}{d x}

\int e^{3 x} sin (x) d x

x^{4} - 8 x^{3} + 7 x^{2} - 4, at x = 1

What is the derivative of (4x-7)/(x^2-1) ?
The derivative of (4x-7)/(x^2-1) is (-4x^2+14x-4)/((x^2-1)^2)
What is the first derivative of (4x-7)/(x^2-1) ?
The first derivative of (4x-7)/(x^2-1) is (-4x^2+14x-4)/((x^2-1)^2)