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

Lösung

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

\frac{y ^{\frac{1}{4}}}{4 x ^{\frac{3}{4}}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

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

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

\int \frac{5 ^{x}}{ln ( 5 )} d x

x \to \infty lim (20)

t an g e n t y = \frac{1}{x ^{2}}, (- 2, \frac{1}{4})

x \to - \infty lim (3^{5 x})

\int \frac{sin ^{3} ( x )}{cos ^{6} ( x )} d x