What is the derivative of ((-48x))/((x^2-16)^2) ?

The derivative of ((-48x))/((x^2-16)^2) is -(48(-3x^2-16))/((x^2-16)^3)

What is the first derivative of ((-48x))/((x^2-16)^2) ?

The first derivative of ((-48x))/((x^2-16)^2) is -(48(-3x^2-16))/((x^2-16)^3)

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derivative of

\frac{( - 48 x )}{( x ^{2} - 16 ) ^{2}}

- \frac{48 ( - 3 x ^{2} - 16 )}{( x ^{2} - 16 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{- 48 x}{( x ^{2} - 16 ) ^{2}})

Simplify

\frac{- 48 x}{( x ^{2} - 16 ) ^{2}} : - \frac{48 x}{( x ^{2} - 16 ) ^{2}}

= \frac{d}{d x} (- \frac{48 x}{( x ^{2} - 16 ) ^{2}})

Take the constant out:

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

= - 48 \frac{d}{d x} (\frac{x}{( x ^{2} - 16 ) ^{2}})

Apply the Quotient Rule:

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

= - 48 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 16 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 16 ) ^{2} ) x}{( ( x ^{2} - 16 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} - 16)^{2}) = 4 x (x^{2} - 16)

= - 48 \cdot \frac{1 \cdot ( x ^{2} - 16 ) ^{2} - 4 x ( x ^{2} - 16 ) x}{( ( x ^{2} - 16 ) ^{2} ) ^{2}}

Simplify

- 48 \cdot \frac{1 \cdot ( x ^{2} - 16 ) ^{2} - 4 x ( x ^{2} - 16 ) x}{( ( x ^{2} - 16 ) ^{2} ) ^{2}} : - \frac{48 ( - 3 x ^{2} - 16 )}{( x ^{2} - 16 ) ^{3}}

= - \frac{48 ( - 3 x ^{2} - 16 )}{( x ^{2} - 16 ) ^{3}}

What is the derivative of ((-48x))/((x^2-16)^2) ?
The derivative of ((-48x))/((x^2-16)^2) is -(48(-3x^2-16))/((x^2-16)^3)
What is the first derivative of ((-48x))/((x^2-16)^2) ?
The first derivative of ((-48x))/((x^2-16)^2) is -(48(-3x^2-16))/((x^2-16)^3)