derivative of sin(x(1+cos(x)))

Lösung

\frac{d}{d x} (sin (x) (1 + cos (x)))

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

Schritte zur Lösung

\frac{d}{d x} (sin (x) (1 + cos (x)))

Wende die Produktregel an:

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

f = sin (x), g = 1 + cos (x)

= \frac{d}{d x} (sin (x)) (1 + cos (x)) + \frac{d}{d x} (1 + cos (x)) sin (x)

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

\frac{d}{d x} (1 + cos (x)) = - sin (x)

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

Vereinfache

cos (x) (1 + cos (x)) + (- sin (x)) sin (x) : cos (x) (1 + cos (x)) - sin^{2} (x)

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

\frac{d}{d x} (sin (3 x + 4 y))

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

d er i v a t i v e cos^{2} (z)

\int x (y) d x

\frac{d}{d x} (x^{4} ln (x) - \frac{1}{3} x^{3})