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

Lösung

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

\frac{x ^{2} + 4 x - 5}{( x + 2 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 ( x - 1 ) ( x + 2 ) - 1 \cdot ( x - 1 ) ^{2}}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x - 5}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x - 5}{( x + 2 ) ^{2}}

\int (e^{2 x} + x) d x

d er i v a t i v e - 0.0000272 x^{2} + 0.008459 x + 440

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

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

\frac{\partial}{\partial x} (sec (x))