derivative of ((x^2+x)/(x^2))

Lösung

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

- \frac{1}{x ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= - \frac{1}{x ^{2}}

\int (x^{5} - 10 x^{4} + x^{3} - 15 x^{2}) d x

n = 1 \sum \infty \frac{z ^{n}}{n ^{2}}

\frac{d y}{d x} = x + 3

x \to 2 lim (4 x)

\int_{1}^{4} (\frac{1}{x})^{2} d x