derivative of (sin(x+cos(x))^3)

Lösung

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

3 (1 + sin (2 x)) (cos (x) - sin (x))

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

(sin (x) + cos (x))^{2} = 1 + sin (2 x)

= 3 (1 + sin (2 x)) (cos (x) - sin (x))

d er i v a t i v e (\frac{1}{2} x)^{3}

\int_{4}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

\frac{d}{d x} (\frac{1}{a} sin (b + a x))

\int e^{5 x} cos (x) d x

\frac{d}{d x} (\frac{8 x + 1}{x ^{- 5}})