d/(dy)(1/(sqrt(x^2+y^2)))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int 64 - t^{2} d t

\frac{d}{d x} (- 6 e^{- x})

t an g e n t f (x)^{8} x^{2} + 4 x - 7, x = - 3

\int sec^{2} (x t a) n^{5} x d x

d er i v a t i v e (\frac{1}{y ^{2}} - \frac{5}{y ^{4}}) (y + 3 y^{3})