(\partial)/(\partial y)(7ln(2x^5-3y))

Lösung

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))

- \frac{21}{2 x ^{5} - 3 y}

Schritte zur Lösung

\frac{\partial}{\partial y} (7 ln (2 x^{5} - 3 y))

Behandle

x

als Konstante

Entferne die Konstante:

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

= 7 \frac{\partial}{\partial y} (ln (2 x^{5} - 3 y))

Wende die Kettenregel an:

\frac{1}{2 x ^{5} - 3 y} \frac{\partial}{\partial y} (2 x^{5} - 3 y)

= \frac{1}{2 x ^{5} - 3 y} \frac{\partial}{\partial y} (2 x^{5} - 3 y)

\frac{\partial}{\partial y} (2 x^{5} - 3 y) = - 3

= 7 \cdot \frac{1}{2 x ^{5} - 3 y} (- 3)

Vereinfache

7 \cdot \frac{1}{2 x ^{5} - 3 y} (- 3) : - \frac{21}{2 x ^{5} - 3 y}

= - \frac{21}{2 x ^{5} - 3 y}

a re a \frac{1}{10 x ^{2}}, x, \frac{x}{10}

\frac{d y}{d x} = k y

\frac{\partial}{\partial x} (e^{x} \cdot cos (x))

d er i v a t i v e 9 (x^{6} - 2)^{5}

\frac{d}{d x} (\frac{x ^{2} - 1}{x + 1})