(\partial)/(\partial y)(arctan(x+8y))

Lösung

\frac{\partial}{\partial y} (arctan (x + 8 y))

\frac{8}{( x + 8 y ) ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial y} (arctan (x + 8 y))

Behandle

x

als Konstante

Wende die Kettenregel an:

\frac{1}{( x + 8 y ) ^{2} + 1} \frac{\partial}{\partial y} (x + 8 y)

= \frac{1}{( x + 8 y ) ^{2} + 1} \frac{\partial}{\partial y} (x + 8 y)

\frac{\partial}{\partial y} (x + 8 y) = 8

= \frac{1}{( x + 8 y ) ^{2} + 1} \cdot 8

Vereinfache

\frac{1}{( x + 8 y ) ^{2} + 1} \cdot 8 : \frac{8}{( x + 8 y ) ^{2} + 1}

= \frac{8}{( x + 8 y ) ^{2} + 1}

\frac{d}{d x} (\frac{1 - 3 x}{4 + x})

d er i v a t i v e y = 9 x^{2} e^{x}

n = 1 \sum \infty (- 5)^{- n}

\frac{d}{d x} (sin^{2} (x) + 2^{s i n (x)})

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