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

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

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

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

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

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

Solution steps

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

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

\frac{d}{d 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}}

\int (π - x) cos (π x) d x

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

y^{^{''}} - 4 y^{^{'}} - 12 y = 0

2 y

\frac{d y}{d x}, y = arccos (4 x^{2})

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