derivative of x^{2/3}+y^{2/3}

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

\int \frac{1}{ln ( x ^{2} )} d x

n = 1 \sum \infty \frac{3 ^{n}}{5 ^{n}}

x \to 0 lim (\frac{9 + x}{x ^{3}})

\frac{\partial}{\partial x} ((2 x^{2} - 5 x)^{3} (2 x + 1))