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

The derivative of-(6x)/((x^2-4)^2) is -(6(-3x^2-4))/((x^2-4)^3)

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

The first derivative of-(6x)/((x^2-4)^2) is -(6(-3x^2-4))/((x^2-4)^3)

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derivative of

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

- \frac{6 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

Solution steps

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

Take the constant out:

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

= - 6 \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}}

= - 6 \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)

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

Simplify

- 6 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}} : - \frac{6 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

= - \frac{6 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

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

\frac{\partial}{\partial x} (x arctan (y))

n = 3 \sum \infty (\frac{9}{11})^{- n}

\int cos^{5} (4 - x) sin (4 - x) d x

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

What is the derivative of-(6x)/((x^2-4)^2) ?
The derivative of-(6x)/((x^2-4)^2) is -(6(-3x^2-4))/((x^2-4)^3)
What is the first derivative of-(6x)/((x^2-4)^2) ?
The first derivative of-(6x)/((x^2-4)^2) is -(6(-3x^2-4))/((x^2-4)^3)