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

Lösung

ableitung von

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

\frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

Schritte zur Lösung

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

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

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

\frac{d}{d x} (5 + x) = 1

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

Vereinfache

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

= \frac{10 x + x ^{2}}{( 5 + x ) ^{2}}

\frac{d y}{d x} + \frac{y}{x} = 2 x^{2} y^{2}

\frac{d y}{d x} + y = x y^{4}

\int_{0}^{2 π} sin^{2} (θ) d θ

t an g e n t f (x) = 2 x^{2} - 5 x

\frac{d}{d x} (- 4 sin (x) + 9 x)