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

The derivative of (4x^2/(x^2-1)) is -(8x)/((x^2-1)^2)

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

The first derivative of (4x^2/(x^2-1)) is -(8x)/((x^2-1)^2)

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

- \frac{8 x}{( x ^{2} - 1 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

4 \cdot \frac{2 x ( x ^{2} - 1 ) - 2 x x ^{2}}{( x ^{2} - 1 ) ^{2}} : - \frac{8 x}{( x ^{2} - 1 ) ^{2}}

= - \frac{8 x}{( x ^{2} - 1 ) ^{2}}

x^{3} + 7 x - 6

3 x

\int \frac{1}{z ^{2} - 1} d z

f (x) = (6 x^{2} - 10 x) e^{x}

\int (sec^{2} (θ) + 5) d θ

What is the derivative of (4x^2/(x^2-1)) ?
The derivative of (4x^2/(x^2-1)) is -(8x)/((x^2-1)^2)
What is the first derivative of (4x^2/(x^2-1)) ?
The first derivative of (4x^2/(x^2-1)) is -(8x)/((x^2-1)^2)