derivative of 3*e^{(x^3/9})

Lösung

\frac{d}{d x} (3 \cdot e^{\frac{x ^{3}}{9}})

e^{\frac{x ^{3}}{9}} x^{2}

Schritte zur Lösung

\frac{d}{d x} (3 e^{\frac{x ^{3}}{9}})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (e^{\frac{x ^{3}}{9}})

Wende die Kettenregel an:

e^{\frac{x ^{3}}{9}} \frac{d}{d x} (\frac{x ^{3}}{9})

= e^{\frac{x ^{3}}{9}} \frac{d}{d x} (\frac{x ^{3}}{9})

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

= 3 e^{\frac{x ^{3}}{9}} \frac{x ^{2}}{3}

Vereinfache

3 e^{\frac{x ^{3}}{9}} \frac{x ^{2}}{3} : e^{\frac{x ^{3}}{9}} x^{2}

= e^{\frac{x ^{3}}{9}} x^{2}

\int (9 x - 2)^{- 3} d x

\int 5 r e^{\frac{r}{2}} d r

d er i v a t i v e f (x) = x^{2} ln (8 - 5 x^{2})

a re a y = x^{3} - 10 x, y = 6 x

\frac{d y}{d x} = x^{6} y^{- 5}