derivative 1/27 (9x^2+6)^{3/2}

Lösung

ableitung von

\frac{1}{27} (9 x^{2} + 6)^{\frac{3}{2}}

x (9 x^{2} + 6)^{\frac{1}{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{27} (9 x^{2} + 6)^{\frac{3}{2}})

Entferne die Konstante:

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

= \frac{1}{27} \frac{d}{d x} ((9 x^{2} + 6)^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( 9 x ^{2} + 6 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (9 x^{2} + 6)

= \frac{3 ( 9 x ^{2} + 6 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (9 x^{2} + 6)

\frac{d}{d x} (9 x^{2} + 6) = 18 x

= \frac{1}{27} \cdot \frac{3 ( 9 x ^{2} + 6 ) ^{\frac{1}{2}}}{2} \cdot 18 x

Vereinfache

\frac{1}{27} \cdot \frac{3 ( 9 x ^{2} + 6 ) ^{\frac{1}{2}}}{2} \cdot 18 x : x (9 x^{2} + 6)^{\frac{1}{2}}

= x (9 x^{2} + 6)^{\frac{1}{2}}

x \to \infty lim (\frac{x}{3})

\int \frac{1}{e ^{x} + 1} d x

n = 0 \sum \infty \frac{1}{( 2 n + 1 ) ^{3}}

n \to \infty lim (- 7^{n})

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 100 )}