What is the derivative of (4x^2-3/(x^2-1)) ?

The derivative of (4x^2-3/(x^2-1)) is -(2x)/((x^2-1)^2)

What is the first derivative of (4x^2-3/(x^2-1)) ?

The first derivative of (4x^2-3/(x^2-1)) is -(2x)/((x^2-1)^2)

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\frac{d}{d x} (\frac{4 x ^{2} - 3}{x ^{2} - 1})

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

Solution steps

\frac{d}{d x} (\frac{4 x ^{2} - 3}{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 ^{2} - 3 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( 4 x ^{2} - 3 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (4 x^{2} - 3) = 8 x

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

= \frac{8 x ( x ^{2} - 1 ) - 2 x ( 4 x ^{2} - 3 )}{( x ^{2} - 1 ) ^{2}}

Simplify

\frac{8 x ( x ^{2} - 1 ) - 2 x ( 4 x ^{2} - 3 )}{( x ^{2} - 1 ) ^{2}} : - \frac{2 x}{( x ^{2} - 1 ) ^{2}}

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

\int (a + b x^{3})^{3} d x

\frac{d}{d x} (2 x - 3 sin (x))

x \to 3 lim (- 2 x^{3})

\int \frac{( x ^{2} - 16 )}{x ^{3}} d x

\frac{1}{x + 4}

What is the derivative of (4x^2-3/(x^2-1)) ?
The derivative of (4x^2-3/(x^2-1)) is -(2x)/((x^2-1)^2)
What is the first derivative of (4x^2-3/(x^2-1)) ?
The first derivative of (4x^2-3/(x^2-1)) is -(2x)/((x^2-1)^2)