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

Lösung

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

\frac{3 x ^{2} + 4 x}{2 ( x + 1 ) x + 1}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 x x + 1 - \frac{1}{2 x + 1} x ^{2}}{( x + 1 ) ^{2}} : \frac{3 x ^{2} + 4 x}{2 ( x + 1 ) x + 1}

= \frac{3 x ^{2} + 4 x}{2 ( x + 1 ) x + 1}

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

x \to - 1 lim (\frac{4 x - 5}{3 - x})

t an g e n t f (x) = x^{2} - x + 19, at x = 3

t an g e n t f (x) = (x - 1) (x - 3)^{2}, at x = 4

(1 + 2 y) d x - (4 - x) d y = 0