d/(d{y)}(sqrt({x)+{y}{z}})

Lösung

\frac{d}{d y} (x + y z)

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

Schritte zur Lösung

\frac{d}{d y} (x + y z)

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \cdot y^{^{'}} = 1 - y^{2}

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

\frac{d}{d x} (\frac{a x + b y ( x )}{c x + d y})

\frac{d}{d x} (\frac{e ^{x} - 1}{e ^{x} + 1})

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