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

Lösung

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

\frac{cos ^{3} ( x ) + sin ( 2 x ) sin ( x )}{2 cos ^{4} ( x )}

Schritte zur Lösung

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

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (\frac{sin ( x )}{cos ^{2} ( x )})

Wende die Quotientenregel an:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( sin ( x ) ) cos ^{2} ( x ) - \frac{d}{d x} ( cos ^{2} ( x ) ) sin ( x )}{( cos ^{2} ( x ) ) ^{2}}

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

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

= \frac{1}{2} \cdot \frac{cos ( x ) cos ^{2} ( x ) - ( - sin ( 2 x ) ) sin ( x )}{( cos ^{2} ( x ) ) ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{cos ( x ) cos ^{2} ( x ) - ( - sin ( 2 x ) ) sin ( x )}{( cos ^{2} ( x ) ) ^{2}} : \frac{cos ^{3} ( x ) + sin ( 2 x ) sin ( x )}{2 cos ^{4} ( x )}

= \frac{cos ^{3} ( x ) + sin ( 2 x ) sin ( x )}{2 cos ^{4} ( x )}

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

d er i v a t i v e \frac{x}{x + 1}

\int + \frac{4 y}{1} d y

\int (\frac{1}{6 x ^{3}}) d x

\frac{d}{d x} ((x - 4) \cdot ln (\frac{x}{4}))