derivative (12)/(x^2(x-3))

Lösung

ableitung von

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

- \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{12}{x ^{2} ( x - 3 )})

Entferne die Konstante:

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

= 12 \frac{d}{d x} (\frac{1}{x ^{2} ( x - 3 )})

Wende Exponentenregel an:

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

= 12 \frac{d}{d x} ((x^{2} (x - 3))^{- 1})

Wende die Kettenregel an:

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

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

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

= 12 (- \frac{1}{( x ^{2} ( x - 3 ) ) ^{2}} (3 x^{2} - 6 x))

Vereinfache

12 (- \frac{1}{( x ^{2} ( x - 3 ) ) ^{2}} (3 x^{2} - 6 x)) : - \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

= - \frac{36 ( x - 2 )}{x ^{3} ( x - 3 ) ^{2}}

\int (4 x^{3} y^{2} - 2 x y^{3}) d x

x ln (\frac{x}{y}) d y - y d x = 0

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

\int (8 x^{5} - 8 x^{- 3}) d x

x \to - 4 lim (6 x + 1)