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

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

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

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

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

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

Solution steps

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

Simplify

\frac{- 2 x ^{2}}{x ^{2} - 1} : - \frac{2 x ^{2}}{x ^{2} - 1}

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

2 cot (\frac{x}{8})

x \to - 2 lim (4)

\int \frac{1}{x ^{2} - 225} d x

\frac{\partial}{\partial s} (s + 2 t - u)

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

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