(\partial)/(\partial x)(x^{0.5}y^{0.5}z)

Lösung

\frac{\partial}{\partial x} (x^{0.5} y^{0.5} z)

\frac{0.5 z y ^{\frac{1}{2}}}{x ^{0.5}}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{0.5} y^{0.5} z)

Behandle

y, z

als Konstanten

Entferne die Konstante:

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

= y^{0.5} z \frac{\partial}{\partial x} (x^{0.5})

Wende die Potenzregel an:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= y^{0.5} z \cdot 0.5 x^{0.5 - 1}

Vereinfache

y^{\frac{1}{2}} z \cdot 0.5 x^{0.5 - 1} : \frac{0.5 z y ^{\frac{1}{2}}}{x ^{0.5}}

= \frac{0.5 z y ^{\frac{1}{2}}}{x ^{0.5}}

(x + 2)^{2} y^{^{'}} + 8 y = 5 - 4 x y

x \to 4 lim (x^{2} - 5 x + 7 x^{3})

\frac{d}{d x} (\frac{1}{2 e ^{2}} e^{2 x})

\int \frac{( u ^{2} ) ^{22}}{1 + ( u ^{2} ) ^{22}} d (u^{2})^{2}

x^{6} + y^{5} x^{7} + 3 y^{^{'}} = 0, y (0) = 0