(\partial)/(\partial x)(\sqrt[3]{x^3+y^3})

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{3 ( x ^{3} + y ^{3} ) ^{\frac{2}{3}}} \cdot 3 x^{2} : \frac{x ^{2}}{( x ^{3} + y ^{3} ) ^{\frac{2}{3}}}

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

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

in v erse l a pl a ce \frac{2 s ^{2}}{s ^{4} - 1}

\int_{0}^{1} 2 x (x^{2} + 1)^{2} d x

d er i v a t i v e f (x) = \frac{6}{x ^{2}}

t a y l or x, 64