(\partial)/(\partial u)(warctan(uv))

Lösung

\frac{\partial}{\partial u} (w arctan (uv))

\frac{w v}{u ^{2} v ^{2} + 1}

Schritte zur Lösung

\frac{\partial}{\partial u} (w arctan (uv))

Behandle

w, v

als Konstanten

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= w \frac{\partial}{\partial u} (arctan (uv))

Wende die Kettenregel an:

\frac{1}{( uv ) ^{2} + 1} \frac{\partial}{\partial u} (uv)

= \frac{1}{( uv ) ^{2} + 1} \frac{\partial}{\partial u} (uv)

\frac{\partial}{\partial u} (uv) = v

= w \frac{1}{( uv ) ^{2} + 1} v

Vereinfache

w \frac{1}{( uv ) ^{2} + 1} v : \frac{w v}{u ^{2} v ^{2} + 1}

= \frac{w v}{u ^{2} v ^{2} + 1}

\int \frac{x ^{4}}{1 - x} d x

\frac{\partial}{\partial x} (y - z)

\frac{d}{d u} (e^{u})

l a pl a ce t r an s f or m 5 t - \frac{π}{3}

\frac{d y}{d x} = 4 x (x - 2)