derivative of (sqrt(x)-1/(x-1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int 16 sin^{3} (x co) s^{2} x d x

\int sin (x t) d t

\frac{d}{d x} (x + y + z)

\int \frac{2 x ^{3} + 6 x ^{2} + 7 x + 4}{x ^{2} + 3 x + 2} d x

t an g e n t y = \frac{1}{x}, (1, 1)