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}}

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

\int \frac{e ^{6 x}}{1 + e ^{2 x}} d x

\frac{d y}{d x} = y (2 - y)

\int 2 x (x^{2} + 19)^{14} d x

\int (x^{2} - 5)^{5} 2 x d x