derivative of ((x^2)/(1+x))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to \frac{π}{2} lim (3 sec (x))

\int \frac{tan ( x )}{sin ( 2 x )} d x

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

\frac{\partial}{\partial x} (\frac{1}{2} (x - y)^{2})

t y^{^{'}} + 2 y = 4 t^{2}