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

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (3 x) = 3

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

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

Vereinfache

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

(x^{2} + 4) d y = (2 x - 10 x y) d x

x \to 0 + lim (\frac{( ln ( x ) )}{x})

\frac{d}{d x} (\frac{3}{16 + x ^{4}})

\frac{\partial}{\partial θ} (2 cos (θ))

\int \frac{- 4}{x} d x