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

Lösung

ableitung von

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

- \frac{x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{7}{x}) - \frac{d}{d x} (x)

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

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

= - \frac{7}{x ^{2}} - \frac{1}{2 x}

Vereinfache

- \frac{7}{x ^{2}} - \frac{1}{2 x} : - \frac{x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

= - \frac{x ^{\frac{3}{2}} + 14}{2 x ^{\frac{3}{2}} x}

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

d er i v a t i v e (\frac{5 x - 1}{4 x + 2})^{- 5}

x \to 0 - lim (1 - e^{x})

\int_{0}^{3} (10 x - 6 x^{2} + 9) d x

\int cos (t) sin^{7} (t) d t