derivative of (x^3ln(x)/(x+2))

Lösung

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

\frac{2 x ^{3} ln ( x ) + x ^{3} + 6 x ^{2} ln ( x ) + 2 x ^{2}}{( x + 2 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{( 3 x ^{2} ln ( x ) + x ^{2} ) ( x + 2 ) - 1 \cdot x ^{3} ln ( x )}{( x + 2 ) ^{2}} : \frac{2 x ^{3} ln ( x ) + x ^{3} + 6 x ^{2} ln ( x ) + 2 x ^{2}}{( x + 2 ) ^{2}}

= \frac{2 x ^{3} ln ( x ) + x ^{3} + 6 x ^{2} ln ( x ) + 2 x ^{2}}{( x + 2 ) ^{2}}

\int \frac{3}{x x ^{2} - 1} d x

\frac{d}{d x} f (x) = 4 x - 9 x^{2}

\int_{2}^{4} x (\frac{( 2 x - 3 )}{6}) d x

x \to \frac{π}{2} lim (e^{s e c (x)})

in v erse l a pl a ce \frac{3}{( s + 2 ) ^{2}}