derivative of 1-\sqrt[3]{x^2+y^2}

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{2 x + 2 y \frac{d y}{d x}}{3 ( x ^{2} + y ^{2} ) ^{\frac{2}{3}}}

Vereinfache

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

\int sec^{3} (π) x d x

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

y^{^{'}} = 3 y + 6

x \to 0 lim (\frac{x}{x - 2})

\frac{\partial}{\partial x} (x^{2} + y^{10})