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

Lösung

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

\frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{( 2 x + 5 ) ( x + 2 ) - 1 \cdot ( x ^{2} + 5 x )}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

y^{^{''}} - 4 y^{^{'}} + y = 0

\int \frac{1}{9 + x ^{2}} d x

\int_{0}^{2} (2^{x} + 6) d x

\frac{\partial}{\partial v} (a sin (u) cos (v))

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