derivative of (e^{3x^2}/(5x))

Lösung

\frac{d}{d x} (\frac{e ^{3 x^{2}}}{5 x})

\frac{6 e ^{3 x^{2}} x ^{2} - e ^{3 x^{2}}}{5 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{3 x^{2}}}{5 x})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (\frac{e ^{3 x^{2}}}{x})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( e ^{3 x^{2}} ) x - \frac{d x}{d x} e ^{3 x^{2}}}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{1}{5} \cdot \frac{e ^{3 x^{2}} \cdot 6 xx - 1 \cdot e ^{3 x^{2}}}{x ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{e ^{3 x^{2}} \cdot 6 xx - 1 \cdot e ^{3 x^{2}}}{x ^{2}} : \frac{6 e ^{3 x^{2}} x ^{2} - e ^{3 x^{2}}}{5 x ^{2}}

= \frac{6 e ^{3 x^{2}} x ^{2} - e ^{3 x^{2}}}{5 x ^{2}}

d er i v a t i v e f (x) = 16 4 x

\int \frac{sin ^{7} ( 10 x )}{cos ^{4} ( 10 x )} d x

\frac{\partial}{\partial y} (f (x, y) (x + y))

d er i v a t i v e f (x) = x + 13

x y^{^{'}} - y = - 2 x^{2} - 2 x + 1