(\partial)/(\partial x)(arctan(x^2+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{x ^{5}}{4 - x ^{4}}

y^{^{'''}} - 7 y^{^{''}} - 8 y^{^{'}} = 0

t an g e n t f (x) = \frac{2}{x ^{2}}, at x = 1

\frac{d}{d x} (\frac{1}{2} cos^{2} (\frac{x}{2}))

\int x^{3} \cdot cos (x^{2}) d x