derivative of (x^2(2/(x^2)+5/(x^3)))

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

(x^{2}) (\frac{2}{x ^{2}} + \frac{5}{x ^{3}}) : 2 + \frac{5}{x}

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (2) = 0

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

= 0 - \frac{5}{x ^{2}}

Vereinfache

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

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

\frac{d}{d x} (x^{\frac{4}{5}} (x - 2)^{2})

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

x \to \frac{π}{2} lim (3 sec (x))

\int \frac{tan ( x )}{sin ( 2 x )} d x