derivative of (x^4+2x^2/(x^2))

Lösung

\frac{d}{d x} (\frac{x ^{4} + 2 x ^{2}}{x ^{2}})

2 x

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{4} + 2 x ^{2}}{x ^{2}})

Vereinfache

\frac{x ^{4} + 2 x ^{2}}{x ^{2}} : x^{2} + 2

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= 2 x + 0

Vereinfache

= 2 x

d er i v a t i v e 3 t^{2} - 12

a re a y = x^{2}, y = 4 x - x^{2}

\frac{\partial}{\partial y} ((x + y)^{e^{y^{2}}})

\int_{0}^{4} \frac{1}{x} d x

x \to \infty lim (3 x - 4)