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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

d er i v a t i v e f (x) = (x - 2)^{3} + 10

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

d er i v a t i v e f (x) = ln (x e^{- 3 x})

\int \frac{1}{x ln ( 2 x )} d x

\frac{d ^{2}}{d y d x} (sin (x^{2} y^{2}))