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

The derivative of-(4x/((x^2-4)^2)) is -(4(-3x^2-4))/((x^2-4)^3)

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

The first derivative of-(4x/((x^2-4)^2)) is -(4(-3x^2-4))/((x^2-4)^3)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{3})

\frac{A}{y ^{7}} + B e^{y}

n = 1 \sum \infty \frac{3 - 2 n}{4 n}

(- 2, 7), (2, 3)

\int sin^{4} (a x) d x

What is the derivative of-(4x/((x^2-4)^2)) ?
The derivative of-(4x/((x^2-4)^2)) is -(4(-3x^2-4))/((x^2-4)^3)
What is the first derivative of-(4x/((x^2-4)^2)) ?
The first derivative of-(4x/((x^2-4)^2)) is -(4(-3x^2-4))/((x^2-4)^3)