(\partial)/(\partial x)((x^{5/7})/(e^x))

Lösung

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

\frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x ^{\frac{5}{7}}}{e ^{x}})

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( x ^{\frac{5}{7}} ) e ^{x} - \frac{\partial}{\partial x} ( e ^{x} ) x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}}

\frac{\partial}{\partial x} (x^{\frac{5}{7}}) = \frac{5}{7 x ^{\frac{2}{7}}}

\frac{\partial}{\partial x} (e^{x}) = e^{x}

= \frac{\frac{5}{7 x ^{\frac{2}{7}}} e ^{x} - e ^{x} x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}}

Vereinfache

\frac{\frac{5}{7 x ^{\frac{2}{7}}} e ^{x} - e ^{x} x ^{\frac{5}{7}}}{( e ^{x} ) ^{2}} : \frac{5 - 7 x}{7 e ^{x} x ^{\frac{2}{7}}}

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

x \to 0 lim (\frac{2}{x ^{2} + x} - \frac{2}{x})

d er i v a t i v e \frac{3 t ^{2} + 4 t - 8}{t ^{\frac{3}{2}}}

x \to 0 lim (x^{3} - 4 x^{2} + 9 x - 2)

\int cos (2 x) d^{2} x d x

y^{^{''}} + 25 y = 0, y (0) = 4.6, y^{^{'}} (0) = - 1.2