(\partial)/(\partial x)(2sqrt(x)y-ye^{y/z})

Lösung

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (y e^{\frac{y}{z}}) = 0

= \frac{y}{x ^{\frac{1}{2}}} - 0

Vereinfache

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

y^{^{'}} = 1 0^{- 21} \cdot y^{3}

x^{3} y^{^{'''}} - x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = x^{3}

d er i v a t i v e \frac{1}{x ^{2} + 3}

d er i v a t i v e 2 3 x

9 y^{^{''}} + y^{^{'}} = 0