(\partial)/(\partial x)(x^{1/2}*y)

Lösung

\frac{\partial}{\partial x} (x^{\frac{1}{2}} \cdot y)

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Potenzregel an:

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

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

Vereinfache

y \frac{1}{2} x^{\frac{1}{2} - 1} : \frac{y}{2 x ^{\frac{1}{2}}}

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

\frac{d}{d x} ((x - \frac{2}{x})^{4})

t an g e n t f (x) = 2 x^{2}, at x = 0

\int 4 x^{- 3} d x

\int \frac{1}{( x + 1 ) ( x - 1 )} d x

d er i v a t i v e f (x) = (2 x - 4) (2 x^{3} - x^{2} + 1)