derivative of (24/(x^2+12))

Lösung

\frac{d}{d x} (\frac{24}{x ^{2} + 12})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{24}{x ^{2} + 12})

Entferne die Konstante:

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

= 24 \frac{d}{d x} (\frac{1}{x ^{2} + 12})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= 24 \frac{d}{d x} ((x^{2} + 12)^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ^{2} + 12 ) ^{2}} \frac{d}{d x} (x^{2} + 12)

= - \frac{1}{( x ^{2} + 12 ) ^{2}} \frac{d}{d x} (x^{2} + 12)

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

= 24 (- \frac{1}{( x ^{2} + 12 ) ^{2}} \cdot 2 x)

Vereinfache

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

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

x \to 1 lim (e^{x} - 1)

\frac{d y}{d t} = \frac{y}{2} + 4 e^{\frac{t}{2}}

y^{^{''''}} - y^{^{''}} + y = 0

d er i v a t i v e f (x) = x^{3} + 6 x^{2} + x df (x)

\int \frac{30}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x