erweitern (cos(x/y)(y-x\frac{dy)/(dx))}{y^2}

Lösung

erweitern

\frac{cos ( \frac{x}{y} ) ( y - x \frac{d y}{d x} )}{y ^{2}}

\frac{cos ( \frac{x}{y} )}{y} - \frac{x cos ( \frac{x}{y} ) \frac{d y}{d x}}{y ^{2}}

Schritte zur Lösung

\frac{cos ( \frac{x}{y} ) ( y - x \frac{d y}{d x} )}{y ^{2}}

Multipliziere aus

cos (\frac{x}{y}) (y - x \frac{d y}{d x}) : cos (\frac{x}{y}) y - x cos (\frac{x}{y}) \frac{d y}{d x}

= \frac{cos ( \frac{x}{y} ) y - x cos ( \frac{x}{y} ) \frac{d y}{d x}}{y ^{2}}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{cos ( \frac{x}{y} ) y - x cos ( \frac{x}{y} ) \frac{d y}{d x}}{y ^{2}} = \frac{cos ( \frac{x}{y} ) y}{y ^{2}} - \frac{x cos ( \frac{x}{y} ) \frac{d y}{d x}}{y ^{2}}

= \frac{cos ( \frac{x}{y} ) y}{y ^{2}} - \frac{x cos ( \frac{x}{y} ) \frac{d y}{d x}}{y ^{2}}

Streiche

\frac{cos ( \frac{x}{y} ) y}{y ^{2}} : \frac{cos ( \frac{x}{y} )}{y}

= \frac{cos ( \frac{x}{y} )}{y} - \frac{x cos ( \frac{x}{y} ) \frac{d y}{d x}}{y ^{2}}

e x p an d (20 G (C) - 80 C = 4, 6) (100 G (C) - 160 C = 140)

e x p an d (\frac{1}{2} \cdot x - \frac{1}{2})^{10}

e x p an d x^{\frac{3}{5}} (x - 8)

e x p an d \frac{x}{( 0.1111 - 2 x ) ^{2}}

e x p an d lo g_{8} (64)