derivative of (x-3/(sqrt(x)-\sqrt{3)})

Lösung

\frac{d}{d x} (\frac{x - 3}{x - 3})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x - 3}{x - 3})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e 100 + 0.4 x^{2}

d er i v a t i v e f (x) = 8 + x tan (x)

t an g e n t f (x) = 3 e^{x} cos (x), (0, 3)

\int 2 e^{- 2 t} + 5 e^{- 8 t} d t

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