derivative of ((sin(x)/(cos(2x)))^3)

Lösung

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

3 sin^{2} (x) cos (x) sec^{3} (2 x) + 6 sec^{3} (2 x) tan (2 x) sin^{3} (x)

Schritte zur Lösung

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

Vereinfache

(\frac{sin ( x )}{cos ( 2 x )})^{3} : sin^{3} (x) sec^{3} (2 x)

= \frac{d}{d x} (sin^{3} (x) sec^{3} (2 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin^{3} (x), g = sec^{3} (2 x)

= \frac{d}{d x} (sin^{3} (x)) sec^{3} (2 x) + \frac{d}{d x} (sec^{3} (2 x)) sin^{3} (x)

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

\frac{d}{d x} (sec^{3} (2 x)) = 6 sec^{3} (2 x) tan (2 x)

= 3 sin^{2} (x) cos (x) sec^{3} (2 x) + 6 sec^{3} (2 x) tan (2 x) sin^{3} (x)

f^{^{'}} (x) = 3 cos (x) + 4 (- sin (x))

x \to 0 + lim (\frac{2}{ln ( x )})

in v erse l a pl a ce \frac{1}{s ^{4} + 1}

\int_{0}^{\frac{π}{2}} cos (2 x) d x

\frac{d}{d x} (\frac{1}{4} cos (\frac{x}{4}))