d/(dy)(2/3 (y-1)^{3/2})

Lösung

\frac{d}{d y} (\frac{2}{3} (y - 1)^{\frac{3}{2}})

(y - 1)^{\frac{1}{2}}

Schritte zur Lösung

\frac{d}{d y} (\frac{2}{3} (y - 1)^{\frac{3}{2}})

Entferne die Konstante:

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

= \frac{2}{3} \frac{d}{d y} ((y - 1)^{\frac{3}{2}})

Wende die Kettenregel an:

\frac{3 ( y - 1 ) ^{\frac{1}{2}}}{2} \frac{d}{d y} (y - 1)

= \frac{3 ( y - 1 ) ^{\frac{1}{2}}}{2} \frac{d}{d y} (y - 1)

\frac{d}{d y} (y - 1) = 1

= \frac{2}{3} \cdot \frac{3 ( y - 1 ) ^{\frac{1}{2}}}{2} \cdot 1

Vereinfache

\frac{2}{3} \cdot \frac{3 ( y - 1 ) ^{\frac{1}{2}}}{2} \cdot 1 : (y - 1)^{\frac{1}{2}}

= (y - 1)^{\frac{1}{2}}

\frac{\partial}{\partial x} ((x - 2)^{2})

x y^{^{'}} + 2 y \cdot ln (x) = 3

\int_{0}^{1} sin (nπ x) d x

in v erse l a pl a ce \frac{3}{s} + \frac{24}{s ^{4}}

\frac{\partial}{\partial y} (4 x^{3} y^{2})