(\partial)/(\partial y)(m/y-625 y/x)

Lösung

\frac{\partial}{\partial y} (\frac{m}{y} - 625 \frac{y}{x})

- \frac{m}{y ^{2}} - \frac{625}{x}

Schritte zur Lösung

\frac{\partial}{\partial y} (\frac{m}{y} - 625 \cdot \frac{y}{x})

Vereinfache

\frac{m}{y} - 625 \cdot \frac{y}{x} : \frac{m}{y} - \frac{625 y}{x}

= \frac{\partial}{\partial y} (\frac{m}{y} - \frac{625 y}{x})

Behandle

m, x

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (\frac{m}{y}) - \frac{\partial}{\partial y} (\frac{625 y}{x})

\frac{\partial}{\partial y} (\frac{m}{y}) = - \frac{m}{y ^{2}}

\frac{\partial}{\partial y} (\frac{625 y}{x}) = \frac{625}{x}

= - \frac{m}{y ^{2}} - \frac{625}{x}

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

\frac{d}{d x} (1 - \frac{3}{y} + x)

\int \frac{x ^{3} - 1}{x ^{4} - 4 x + 1} d x

\frac{d}{d x} (- 4 sec^{2} (x) + 6 sec^{4} (x))

x \to 3 lim (- 3 x - 7)