What is (\partial)/(\partial x)((x^2)/(x^2-1)) ?

The answer to (\partial)/(\partial x)((x^2)/(x^2-1)) is -(2x)/((x^2-1)^2)

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(\partial)/(\partial x)((x^2)/(x^2-1))

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

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

Solution steps

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

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

\frac{\partial}{\partial 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}}

f (x) = 4 x, at x = 1

\frac{\partial}{\partial x} (2 x^{2} - 16 x + y^{2} + 1)

\frac{\partial}{\partial x} (e^{t} x + 1)

\int x^{2} e^{x - 3} d x

What is (\partial)/(\partial x)((x^2)/(x^2-1)) ?
The answer to (\partial)/(\partial x)((x^2)/(x^2-1)) is -(2x)/((x^2-1)^2)