(\partial)/(\partial y)(arctan(xy^2))

Lösung

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

\frac{2 x y}{x ^{2} y ^{4} + 1}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{( x y ^{2} ) ^{2} + 1} \cdot 2 x y : \frac{2 x y}{x ^{2} y ^{4} + 1}

= \frac{2 x y}{x ^{2} y ^{4} + 1}

\int 2 t e^{2 t} d t

x \to 0 - lim (\frac{3}{e ^{x} + 1})

\frac{\partial}{\partial y} ((\frac{x}{y}) e^{x y})

\frac{\partial}{\partial z} (e^{x} sin (y))

y^{^{''}} - 10 y^{^{'}} + 25 y = t^{- 8} e^{5 t}