d/(dy)(arctan(x+2y))

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 2 lim (20 - x^{2})

\frac{d}{d x} (x - 2)

\int \frac{1}{7 x + 5} d x

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

\int \frac{e ^{2 x}}{( 1 + e ^{2 x} ) ^{3}} d x