derivative of (x+3/(sqrt(x)))

Lösung

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

\frac{x - 3}{2 x x}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

= \frac{x - 3}{2 x x}

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

x \to \infty lim (- 5 x)

x^{4} + y^{3} x^{5} + 4 y^{^{'}} = 0, y (0) = 0

\frac{\partial}{\partial x} (\frac{x y}{x ^{2} + y ^{2}})

d er i v a t i v e 7 (e^{x} cos (x) - e^{x} sin (x))