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)

sin (x) sin (x) = sin^{2} (x)

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

n = 0 \sum \infty \frac{1}{2 - e ^{- n}}

d er i v a t i v e f (x) = - 10 x sin (5 x^{2} + 5)

\frac{d}{d x} ((4 - x^{\frac{2}{3}})^{\frac{2}{3}})

\int \frac{x - 11}{x ^{2} + 6 x + 25} d x

\int \frac{x ^{2} - 7 x + 12}{x - 3} d x