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

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

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

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

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Popular >

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

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

Solution steps

\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}}

= \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

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

Simplify

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

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

\frac{d}{d x} (lo g_{3} (x^{2}))

x \to 0 lim (\frac{1}{ln ( x ^{3} )})

\int 9 + sin (x) d x

\int_{0}^{1.25} 1250 x d x

\int \frac{16 x ^{3} - 32 x ^{2} + 7}{x ^{2} - 2 x} d x

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