(\partial)/(\partial x)(25x^{(3/4)}y^{1/4})

Lösung

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

\frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

Schritte zur Lösung

\frac{\partial}{\partial x} (25 x^{(\frac{3}{4})} y^{\frac{1}{4}})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 25 y^{\frac{1}{4}} \frac{\partial}{\partial x} (x^{\frac{3}{4}})

Wende die Potenzregel an:

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

= 25 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1}

Vereinfache

25 y^{\frac{1}{4}} \frac{3}{4} x^{\frac{3}{4} - 1} : \frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

= \frac{75 y ^{\frac{1}{4}}}{4 x ^{\frac{1}{4}}}

y^{^{'}} + \frac{2 ( y - 1 )}{x} = 0

\int_{0}^{1} e^{2 x} d x

a re a 15 - x^{2}, x^{2} - 3

n = 1 \sum \infty 2 e^{- 9 n}

\int t e^{8 t} d t