derivative of (x+6/(5x^2e^x))

Lösung

\frac{d}{d x} (\frac{x + 6}{5 x ^{2} e ^{x}})

- \frac{x ^{2} + 7 x + 12}{5 e ^{x} x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 6}{5 x ^{2} e ^{x}})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (\frac{x + 6}{x ^{2} e ^{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} ( x + 6 ) x ^{2} e ^{x} - \frac{d}{d x} ( x ^{2} e ^{x} ) ( x + 6 )}{( x ^{2} e ^{x} ) ^{2}}

\frac{d}{d x} (x + 6) = 1

\frac{d}{d x} (x^{2} e^{x}) = 2 x e^{x} + e^{x} x^{2}

= \frac{1}{5} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 6 )}{( x ^{2} e ^{x} ) ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{1 \cdot x ^{2} e ^{x} - ( 2 x e ^{x} + e ^{x} x ^{2} ) ( x + 6 )}{( x ^{2} e ^{x} ) ^{2}} : - \frac{x ^{2} + 7 x + 12}{5 e ^{x} x ^{3}}

= - \frac{x ^{2} + 7 x + 12}{5 e ^{x} x ^{3}}

d er i v a t i v e f (x) = - cos (x)

x \to 16 lim (x - 164)

\frac{\partial}{\partial x} (arctan (x^{2} + y^{2}))

d er i v a t i v e \frac{x ^{5}}{4 - x ^{4}}

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} = 0