derivative of-(48x/((x^2+12)^2))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

(\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}}

Vereinfache

- 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

d er i v a t i v e \frac{1}{sin ( x )}

\int sin (2 θ) sin (6 θ) d θ

l a pl a ce t r an s f or m 2 sin (3 t) cos (3 t)

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