What is the derivative of (x^2+5/(x^2-1)) ?

The derivative of (x^2+5/(x^2-1)) is -(12x)/((x^2-1)^2)

What is the first derivative of (x^2+5/(x^2-1)) ?

The first derivative of (x^2+5/(x^2-1)) is -(12x)/((x^2-1)^2)

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\frac{d}{d x} (\frac{x ^{2} + 5}{x ^{2} - 1})

- \frac{12 x}{( x ^{2} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 5}{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} + 5 ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( x ^{2} + 5 )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (x^{2} + 5) = 2 x

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

= \frac{2 x ( x ^{2} - 1 ) - 2 x ( x ^{2} + 5 )}{( x ^{2} - 1 ) ^{2}}

Simplify

\frac{2 x ( x ^{2} - 1 ) - 2 x ( x ^{2} + 5 )}{( x ^{2} - 1 ) ^{2}} : - \frac{12 x}{( x ^{2} - 1 ) ^{2}}

= - \frac{12 x}{( x ^{2} - 1 ) ^{2}}

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

\int_{0}^{1} \frac{61}{4 y - 1} d y

\frac{d y}{d x}, ln (x^{2} - 24 y) = x - y - 4

f (x) = - 2 - 6 x^{2}, (5, - 152)

\int sin (x) cos^{2} (x) d x

What is the derivative of (x^2+5/(x^2-1)) ?
The derivative of (x^2+5/(x^2-1)) is -(12x)/((x^2-1)^2)
What is the first derivative of (x^2+5/(x^2-1)) ?
The first derivative of (x^2+5/(x^2-1)) is -(12x)/((x^2-1)^2)