(\partial)/(\partial y)(arctan(9x-9y))

Lösung

\frac{\partial}{\partial y} (arctan (9 x - 9 y))

- \frac{9}{( 9 x - 9 y ) ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial y} (arctan (9 x - 9 y))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{( 9 x - 9 y ) ^{2} + 1} \frac{\partial}{\partial y} (9 x - 9 y)

= \frac{1}{( 9 x - 9 y ) ^{2} + 1} \frac{\partial}{\partial y} (9 x - 9 y)

\frac{\partial}{\partial y} (9 x - 9 y) = - 9

= \frac{1}{( 9 x - 9 y ) ^{2} + 1} (- 9)

Vereinfache

\frac{1}{( 9 x - 9 y ) ^{2} + 1} (- 9) : - \frac{9}{( 9 x - 9 y ) ^{2} + 1}

= - \frac{9}{( 9 x - 9 y ) ^{2} + 1}

\int sin (x) cos (3 x) d x

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x \to x lim (\frac{1}{x})

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