derivative of \sqrt[3]{sin^2(2x})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (sin^{2} (2 x))

= \frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (sin^{2} (2 x))

\frac{d}{d x} (sin^{2} (2 x)) = 2 sin (4 x)

= \frac{1}{3 ( sin ^{2} ( 2 x ) ) ^{\frac{2}{3}}} \cdot 2 sin (4 x)

Vereinfache

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

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

\int sec (1) d x

x \to \frac{x}{4} lim (\frac{sin ( x )}{x})

\int \frac{π}{2} \frac{π}{32} sec (2 θ) tan (2 θ) d θ

\frac{\partial}{\partial y} (10 e^{x} sin (y) z^{3})

f (θ) = 3 cos (θ)