derivative of \sqrt[4]{x^2+y^2}

Lösung

\frac{d}{d x} (4 x^{2} + y^{2})

\frac{x + y \frac{d y}{d x}}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{4}}}

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} + y^{2})

Wende die Kettenregel an:

\frac{1}{4 ( x ^{2} + y ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{2} + y^{2})

= \frac{1}{4 ( x ^{2} + y ^{2} ) ^{\frac{3}{4}}} \frac{d}{d x} (x^{2} + y^{2})

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

= \frac{1}{4 ( x ^{2} + y ^{2} ) ^{\frac{3}{4}}} (2 x + 2 y \frac{d y}{d x})

Vereinfache

\frac{1}{4 ( x ^{2} + y ^{2} ) ^{\frac{3}{4}}} (2 x + 2 y \frac{d y}{d x}) : \frac{x + y \frac{d y}{d x}}{2 ( x ^{2} + y ^{2} ) ^{\frac{3}{4}}}

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

\frac{d}{d x} (\frac{x ^{4} - x + 1}{x ^{4} + x + 1})

\int cos (x^{3} - 1) d x

x \to 2 lim (- x^{2} + 4 x + 2)

\int (- 2 sin (2 x) + 2 cos (2 x)) d x

h \to 0 lim (\frac{cos ( \frac{π}{6} + h ) - \frac{3}{2}}{h})