derivative of 3x^{-2}-1/x

Lösung

\frac{d}{d x} (3 x^{- 2} - \frac{1}{x})

- \frac{6}{x ^{3}} + \frac{1}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (3 x^{- 2} - \frac{1}{x})

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (3 x^{- 2}) = - \frac{6}{x ^{3}}

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

= - \frac{6}{x ^{3}} - (- \frac{1}{x ^{2}})

Vereinfache

= - \frac{6}{x ^{3}} + \frac{1}{x ^{2}}

(3 x^{2} y^{2}) d x + (2 x^{3} y + 4 y^{3}) d y = 0

x \to - \frac{π}{3} lim (- 2 cos (x))

\frac{d}{d x} (sin (x^{2}) + cos^{2} (x))

\frac{\partial}{\partial x} (\frac{2}{2 x - y})

\int_{1}^{\infty} \frac{1}{x ^{2} + 5} d x