derivative of 2/9 x^3+3x+cos(x+1)

Lösung

\frac{d}{d x} (\frac{2}{9} x^{3} + 3 x + cos (x) + 1)

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{9} x^{3} + 3 x + cos (x) + 1)

Vereinfache

\frac{2}{9} x^{3} + 3 x + cos (x) + 1 : \frac{2 x ^{3}}{9} + 3 x + cos (x) + 1

= \frac{d}{d x} (\frac{2 x ^{3}}{9} + 3 x + cos (x) + 1)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{2 x ^{3}}{9}) + \frac{d}{d x} (3 x) + \frac{d}{d x} (cos (x)) + \frac{d}{d x} (1)

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

\frac{d}{d x} (3 x) = 3

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

\frac{d}{d x} (1) = 0

= \frac{2 x ^{2}}{3} + 3 - sin (x) + 0

Vereinfache

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