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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Vereinfache

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

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

d er i v a t i v e cos (a^{5} + x^{5})

\int \frac{x}{x ^{2} + 16} d x

\frac{\partial}{\partial y} (e^{5 x y})

\int 9^{x} d x

t an g e n t f (x) = 0.14 x^{2} + 0.68 x + 3.1