(\partial)/(\partial x)((xy)^{0.5})

Lösung

\frac{\partial}{\partial x} ((x y)^{0.5})

\frac{0.5 y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

Schritte zur Lösung

\frac{\partial}{\partial x} ((x y)^{0.5})

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{0.5}{( x y ) ^{0.5}} \frac{\partial}{\partial x} (x y)

= \frac{0.5}{( x y ) ^{0.5}} \frac{\partial}{\partial x} (x y)

\frac{\partial}{\partial x} (x y) = y

= \frac{0.5}{( x y ) ^{0.5}} y

Vereinfache

\frac{0.5}{( x y ) ^{\frac{1}{2}}} y : \frac{0.5 y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

= \frac{0.5 y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

l a pl a ce t r an s f or m 80 t^{2}

x \to 0 lim (\frac{( x - 1 ) ^{2} + 1}{x})

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

d er i v a t i v e y = x^{3} + 1

d er i v a t i v e arcsin (\frac{x}{4})