derivative of (1+x/(x^3))

Lösung

\frac{d}{d x} (\frac{1 + x}{x ^{3}})

\frac{- 2 x - 3}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 + x}{x ^{3}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{- 2 x - 3}{x ^{4}}

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

y^{^{'}} + 7 y = e^{6 x}

\int_{0}^{2 π} sin^{2} (x) d x

n = 1 \sum \infty n^{- \frac{1}{5}}

x \to 2 - lim (\frac{5 x}{x - 6})