(\partial)/(\partial x)(4x^{0.5}+2x^{0.25})

Lösung

\frac{\partial}{\partial x} (4 x^{0.5} + 2 x^{0.25})

\frac{2 x ^{0.25} + 0.5}{x ^{0.75}}

Schritte zur Lösung

\frac{\partial}{\partial x} (4 x^{0.5} + 2 x^{0.25})

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (4 x^{0.5}) + \frac{\partial}{\partial x} (2 x^{0.25})

\frac{\partial}{\partial x} (4 x^{0.5}) = \frac{2}{x ^{0.5}}

\frac{\partial}{\partial x} (2 x^{0.25}) = \frac{0.5}{x ^{0.75}}

= \frac{2}{x ^{0.5}} + \frac{0.5}{x ^{0.75}}

Vereinfache

\frac{2}{x ^{\frac{1}{2}}} + \frac{0.5}{x ^{0.75}} : \frac{2 x ^{0.25} + 0.5}{x ^{0.75}}

= \frac{2 x ^{0.25} + 0.5}{x ^{0.75}}

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