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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

d er i v a t i v e y (θ) = \frac{π}{8} sin (θ)

\int \frac{1}{b ^{2} 25 + b ^{2}} d b

\frac{d}{d x} (2 - 4 cos (x))

y^{^{'}} = \frac{x y}{1 - x ^{2}}

f (x) = cos (x^{3})