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

Lösung

ableitung von

\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}

t an g e n t f (x) = x^{2} - 9 x, at x = 3

\frac{\partial}{\partial y} (x^{3} y)

t a y l or \frac{1}{( z + 1 ) ^{3}}

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

(x^{4} + y^{2}) d x - x y d y = 0