derivative (x^3)/((x+1)^2)

Lösung

ableitung von

\frac{x ^{3}}{( x + 1 ) ^{2}}

\frac{x ^{2} ( x + 3 )}{( x + 1 ) ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d θ} (2 cos (θ) + 2 sin (θ))

3 (1 + x^{2}) \frac{d y}{d x} = 2 x y (y^{3} - 1)

in v erse l a pl a ce e^{- 2 s} \cdot \frac{1}{s - 3}

\int \frac{1}{( x ^{2} - 25 ) ^{\frac{1}{2}}} d x

t an g e n t f (x) = - x^{3}, at x = 2