derivative f(x)=(x+7)/(sqrt(x))

Lösung

ableitung von

f (x) = \frac{x + 7}{x}

\frac{x - 7}{2 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 7}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x + 7 ) x - \frac{d}{d x} ( x ) ( x + 7 )}{( x ) ^{2}}

\frac{d}{d x} (x + 7) = 1

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

= \frac{1 \cdot x - \frac{1}{2 x} ( x + 7 )}{( x ) ^{2}}

Vereinfache

\frac{1 \cdot x - \frac{1}{2 x} ( x + 7 )}{( x ) ^{2}} : \frac{x - 7}{2 x x}

= \frac{x - 7}{2 x x}

n = 1 \sum \infty \frac{1}{3 ^{n - 3}}

t an g e n t y = \frac{2 x + 1}{x + 2}, (1, 1)

\frac{\partial}{\partial y} (cos (2 x y))

d er i v a t i v e g (x) = 9 - 2

\int_{- 1}^{1} \frac{5 x}{( x + 3 ) ^{2}} d x