derivative of ((x^2-4^{3/2})/6)

Lösung

\frac{d}{d x} \frac{( x ^{2} - 4 ) ^{\frac{3}{2}}}{6}

\frac{x ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2}

Schritte zur Lösung

\frac{d}{d x} \frac{( x ^{2} - 4 ) ^{\frac{3}{2}}}{6}

Entferne die Konstante:

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

= \frac{1}{6} \frac{d}{d x} ((x^{2} - 4)^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x^{2} - 4)

= \frac{3 ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2} \frac{d}{d x} (x^{2} - 4)

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

= \frac{1}{6} \cdot \frac{3 ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2} \cdot 2 x

Vereinfache

\frac{1}{6} \cdot \frac{3 ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2} \cdot 2 x : \frac{x ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2}

= \frac{x ( x ^{2} - 4 ) ^{\frac{1}{2}}}{2}

n = 0 \sum \infty π

x \to \infty lim (1 - \frac{5}{x})

x \to 3 lim (5 x)

n = 0 \sum \infty (- 1)^{n} n

\int \frac{1}{( 1 - 6 x ) ^{\frac{7}{2}}} d x