derivative of xcos^2(x)

Lösung

\frac{d}{d x} (x cos^{2} (x))

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

Schritte zur Lösung

\frac{d}{d x} (x cos^{2} (x))

Wende die Produktregel an:

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

f = x, g = cos^{2} (x)

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

x \to 1 + lim (\frac{5}{x ^{2} - 1})

\int \frac{1}{1 + 2 x} d x

x \to 3 lim (4 x)

x \to 3 lim (5 x^{3} - 4 x^{2} + x - 6)

\frac{d}{d x} ((a x^{2} + b x + c) e^{- \frac{x}{2}})