derivative of (sin(x)/(y^2))

Lösung

\frac{d}{d x} (\frac{sin ( x )}{y ^{2}})

\frac{cos ( x ) y - 2 sin ( x ) \frac{d y}{d x}}{y ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( x )}{y ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Vereinfache

\frac{cos ( x ) y ^{2} - 2 y \frac{d y}{d x} sin ( x )}{( y ^{2} ) ^{2}} : \frac{cos ( x ) y - 2 sin ( x ) \frac{d y}{d x}}{y ^{3}}

= \frac{cos ( x ) y - 2 sin ( x ) \frac{d y}{d x}}{y ^{3}}

\frac{d}{d x} (3 \cdot ln (x))

\frac{d}{d x} (- 7 x)

l a pl a ce t r an s f or m (1 + e^{2 t})^{2}

2 y^{^{''}} + 12 y^{^{'}} + 50 y = 0

\int cos^{2} (2 x) sin (2 x) d x