derivative of sin^2(2xcos^3(3x))

Lösung

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

2 cos^{3} (3 x) sin (4 x) - 9 cos^{2} (3 x) sin^{2} (2 x) sin (3 x)

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

\frac{d}{d x} (cos^{3} (3 x)) = - 9 cos^{2} (3 x) sin (3 x)

= 2 sin (4 x) cos^{3} (3 x) + (- 9 cos^{2} (3 x) sin (3 x)) sin^{2} (2 x)

Vereinfache

= 2 cos^{3} (3 x) sin (4 x) - 9 cos^{2} (3 x) sin^{2} (2 x) sin (3 x)

x \to \infty lim ((4^{x} + 4^{x})^{\frac{1}{2 x}})

\int \frac{x + 16}{x ^{2} + 2 x - 8} d x

x \to 0 lim (x^{6} cos (\frac{4}{x}))

\int_{0}^{\frac{π}{4}} 7 tan^{3} (x) d x

\int \frac{3 x}{( x ^{2} + 3 ) ^{2}} d x