(\partial)/(\partial x)((x^{0.5}+y^{0.5})^2)

Lösung

\frac{\partial}{\partial x} ((x^{0.5} + y^{0.5})^{2})

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

Schritte zur Lösung

\frac{\partial}{\partial x} ((x^{0.5} + y^{0.5})^{2})

Behandle

y

als Konstante

Wende die Kettenregel an:

2 (x^{0.5} + y^{0.5}) \frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

= 2 (x^{0.5} + y^{0.5}) \frac{\partial}{\partial x} (x^{0.5} + y^{0.5})

\frac{\partial}{\partial x} (x^{0.5} + y^{0.5}) = \frac{0.5}{x ^{\frac{1}{2}}}

= 2 (x^{0.5} + y^{0.5}) \frac{0.5}{x ^{\frac{1}{2}}}

Vereinfache

2 (x^{\frac{1}{2}} + y^{\frac{1}{2}}) \frac{0.5}{x ^{\frac{1}{2}}} : \frac{x ^{\frac{1}{2}} + y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

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