What is the derivative of-(48x/((x^2+12)^2)) ?

The derivative of-(48x/((x^2+12)^2)) is -(144(-x^2+4))/((x^2+12)^3)

What is the first derivative of-(48x/((x^2+12)^2)) ?

The first derivative of-(48x/((x^2+12)^2)) is -(144(-x^2+4))/((x^2+12)^3)

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\frac{d}{d x} (- \frac{48 x}{( x ^{2} + 12 ) ^{2}})

- \frac{144 ( - x ^{2} + 4 )}{( x ^{2} + 12 ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{48 x}{( x ^{2} + 12 ) ^{2}})

Take the constant out:

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

= - 48 \frac{d}{d x} (\frac{x}{( x ^{2} + 12 ) ^{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} + 12 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 12 ) ^{2} ) x}{( ( x ^{2} + 12 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} + 12)^{2}) = 4 x (x^{2} + 12)

= - 48 \cdot \frac{1 \cdot ( x ^{2} + 12 ) ^{2} - 4 x ( x ^{2} + 12 ) x}{( ( x ^{2} + 12 ) ^{2} ) ^{2}}

Simplify

- 48 \cdot \frac{1 \cdot ( x ^{2} + 12 ) ^{2} - 4 x ( x ^{2} + 12 ) x}{( ( x ^{2} + 12 ) ^{2} ) ^{2}} : - \frac{144 ( - x ^{2} + 4 )}{( x ^{2} + 12 ) ^{3}}

= - \frac{144 ( - x ^{2} + 4 )}{( x ^{2} + 12 ) ^{3}}

\int e^{i x} d x

\frac{1}{sin ( x )}

\int sin (2 θ) sin (6 θ) d θ

2 sin (3 t) cos (3 t)

\int (z + 3)^{4} d z

What is the derivative of-(48x/((x^2+12)^2)) ?
The derivative of-(48x/((x^2+12)^2)) is -(144(-x^2+4))/((x^2+12)^3)
What is the first derivative of-(48x/((x^2+12)^2)) ?
The first derivative of-(48x/((x^2+12)^2)) is -(144(-x^2+4))/((x^2+12)^3)