derivative f(x)=sqrt(x/(x+3))

Lösung

ableitung von

f (x) = \frac{x}{x + 3}

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{2 \frac{x}{x + 3}} \frac{d}{d x} (\frac{x}{x + 3})

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

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

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

Vereinfache

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

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

n = 1 \sum \infty \frac{( - 1 ) ^{n + 1} 2 n}{n + 1}

\int_{- \frac{π}{4}}^{0} 6 sec^{3} (x) d x

x \to 2 - lim (\frac{∣ x - 2 ∣}{x - 2})

\frac{\partial}{\partial x} (\frac{18 x y}{x + y})

x \to 8 lim (15)