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

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

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

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

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derivative of

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

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

Solution steps

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

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

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

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

Expand

(2 x + 2) (x^{2} - 1) - 2 x (x^{2} + 2 x) : - 2 x^{2} - 2 x - 2

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

\int \frac{1}{1 + 14 x} d x

f (x) = 4 x + 1

x

x^{11} e^{x}

x \to 0 lim (\frac{( 2 + x ) ^{2} - 4}{x})

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