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

The derivative of ((x^2-1))/(x^2-4) is -(6x)/((x^2-4)^2)

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

The first derivative of ((x^2-1))/(x^2-4) is -(6x)/((x^2-4)^2)

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derivative of

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

- \frac{6 x}{( x ^{2} - 4 ) ^{2}}

Solution steps

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

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

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

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

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

Simplify

\frac{2 x ( x ^{2} - 4 ) - 2 x ( x ^{2} - 1 )}{( x ^{2} - 4 ) ^{2}} : - \frac{6 x}{( x ^{2} - 4 ) ^{2}}

= - \frac{6 x}{( x ^{2} - 4 ) ^{2}}

\int \frac{3 x}{π} d x

\frac{\partial}{\partial y} (e^{7 x})

\int \frac{x ^{2}}{x ^{4} + 1} d x

e^{x} y \frac{d y}{d x} = e^{- y} + e^{2 x - y}

\int (x + 3) (x + 1) x (x - 2) d x

What is the derivative of ((x^2-1))/(x^2-4) ?
The derivative of ((x^2-1))/(x^2-4) is -(6x)/((x^2-4)^2)
What is the first derivative of ((x^2-1))/(x^2-4) ?
The first derivative of ((x^2-1))/(x^2-4) is -(6x)/((x^2-4)^2)