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

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

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

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

2 x \frac{d y}{d x} + y^{3} e^{- 2 x} = 2 x y

s im pl i f y cos (x y)

\frac{\partial}{\partial x} (- 10 x e^{- 5 x^{2} - 2 y^{2}})

\int 6 x + 2 d x

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