derivative of (x+5/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{x + 5}{x})

\frac{x - 5}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 5}{x})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x + 5) = 1

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

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

Vereinfache

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

= \frac{x - 5}{2 x x}

x^{2} y^{^{''}} + x y^{^{'}} - y = x^{\frac{1}{2}}

x \to \infty lim (\frac{4 ^{x} + 3}{4 ^{x + 1}})

d er i v a t i v e f (x) = - \frac{2}{x}

\int (csc (x)) d x

\frac{d}{d x} (arctan (- 5 x + 1))