derivative y=3x^3-10x-4/(x^3)

Lösung

ableitung von

y = 3 x^{3} - 10 x - \frac{4}{x ^{3}}

9 x^{2} - 10 + \frac{12}{x ^{4}}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (3 x^{3}) = 9 x^{2}

\frac{d}{d x} (10 x) = 10

\frac{d}{d x} (\frac{4}{x ^{3}}) = - \frac{12}{x ^{4}}

= 9 x^{2} - 10 - (- \frac{12}{x ^{4}})

Vereinfache

= 9 x^{2} - 10 + \frac{12}{x ^{4}}

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

\frac{\partial}{\partial x} (x + 2 y + 1)

h \to 0 lim (\frac{( 2 + h ) ^{2} - 8}{h})

\frac{\partial}{\partial x} (ln (x^{2}))

\frac{\partial}{\partial z} (x z - 5 x^{2} y^{3} z^{4})