(\partial)/(\partial y)(sqrt((2x-3y)^3))

Lösung

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

- \frac{9 2 x - 3 y}{2}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial y} ((2 x - 3 y)^{3}) = - 9 (2 x - 3 y)^{2}

= \frac{1}{2 ( 2 x - 3 y ) ^{3}} (- 9 (2 x - 3 y)^{2})

Vereinfache

\frac{1}{2 ( 2 x - 3 y ) ^{3}} (- 9 (2 x - 3 y)^{2}) : - \frac{9 2 x - 3 y}{2}

= - \frac{9 2 x - 3 y}{2}

a re a x + 8, x = 0, y = 0

d er i v a t i v e y = \frac{x + x ^{2}}{e ^{x} + 1}

\frac{d}{d x} (\frac{54}{x ^{4}})

\int 2 x + 4 x^{2} - \frac{5}{2} d x

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