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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int_{0}^{3} x x^{2} + 1 d x

\int \frac{1}{20 - y} d y

\frac{d}{d x} (sin (ln (x)) + cos (ln (x)))

d er i v a t i v e f (x) = - 3 x^{3}

in v erse l a pl a ce \frac{( s + 6 )}{( s ^{2} + 6 s + 25 )}