derivative of arctan(x^2+y^2)

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

\frac{d}{d y} (y - 1)

\int (\frac{1}{cos ( x )}) d x

t an g e n t 6 - 5 x^{2}

n = 1 \sum \infty \frac{5}{n ^{2} + 9}

\int_{\frac{1}{5}}^{3} 6 x ln (5 x) d x