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

The answer to (\partial)/(\partial x)((x^2+1)/(x^2-1)) is -(4x)/((x^2-1)^2)

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

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

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

Solution steps

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

\frac{\partial}{\partial x} (x^{2} + 1) = 2 x

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

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

Simplify

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

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

x \to 0 - lim (2 x e^{2 x} + k x)

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\frac{\partial}{\partial x} (e^{x + y + 8})

\int_{0}^{2 l n (7)} (5 e^{\frac{x}{2}}) d x

What is (\partial)/(\partial x)((x^2+1)/(x^2-1)) ?
The answer to (\partial)/(\partial x)((x^2+1)/(x^2-1)) is -(4x)/((x^2-1)^2)