What is (\partial)/(\partial x)(-(4x)/((x^2-1)^2)) ?

The answer to (\partial)/(\partial x)(-(4x)/((x^2-1)^2)) is -(4(-3x^2-1))/((x^2-1)^3)

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(\partial)/(\partial x)(-(4x)/((x^2-1)^2))

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

- \frac{4 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

- 4 \cdot \frac{1 \cdot ( x ^{2} - 1 ) ^{2} - 4 x ( x ^{2} - 1 ) x}{( ( x ^{2} - 1 ) ^{2} ) ^{2}} : - \frac{4 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}}

= - \frac{4 ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{3}}

\frac{4}{( s ^{2} + 4 )}

x \to \infty lim (csc (x))

3 \frac{d y}{d x} = x^{2}

\int \frac{x + 8}{3 x ^{2} - 12} d x

\int (\frac{1}{x ( ln ( x ) - 1 )}) d x

What is (\partial)/(\partial x)(-(4x)/((x^2-1)^2)) ?
The answer to (\partial)/(\partial x)(-(4x)/((x^2-1)^2)) is -(4(-3x^2-1))/((x^2-1)^3)