derivative f(x)=2x^{-2}-3x^{-7/3}

Lösung

ableitung von

f (x) = 2 x^{- 2} - 3 x^{- \frac{7}{3}}

\frac{- 4 x ^{\frac{10}{3}} + 7 x ^{3}}{x ^{\frac{19}{3}}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{- 2} - 3 x^{- \frac{7}{3}})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (2 x^{- 2}) - \frac{d}{d x} (3 x^{- \frac{7}{3}})

\frac{d}{d x} (2 x^{- 2}) = - \frac{4}{x ^{3}}

\frac{d}{d x} (3 x^{- \frac{7}{3}}) = - \frac{7}{x ^{\frac{10}{3}}}

= - \frac{4}{x ^{3}} - (- \frac{7}{x ^{\frac{10}{3}}})

Vereinfache

- \frac{4}{x ^{3}} - (- \frac{7}{x ^{\frac{10}{3}}}) : \frac{- 4 x ^{\frac{10}{3}} + 7 x ^{3}}{x ^{\frac{19}{3}}}

= \frac{- 4 x ^{\frac{10}{3}} + 7 x ^{3}}{x ^{\frac{19}{3}}}

\int 3 x x - 5 d x

\frac{\partial}{\partial x} (arcsin (x))

t a y l or x^{2} + 2 x, 1

\frac{\partial}{\partial x} (3 x^{2} y^{2} - 4 y)

x \to \infty lim ((1 + \frac{2}{x + 1})^{x + 1})