derivative of xcos(pix)

Lösung

\frac{d}{d x} (x cos (π x))

cos (π x) - π x sin (π x)

Schritte zur Lösung

\frac{d}{d x} (x cos (π x))

Wende die Produktregel an:

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

f = x, g = cos (π x)

= \frac{d x}{d x} cos (π x) + \frac{d}{d x} (cos (π x)) x

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

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

= 1 \cdot cos (π x) + (- sin (π x) π) x

Vereinfache

= cos (π x) - π x sin (π x)

\int_{- 5}^{5} \frac{1}{x ^{\frac{2}{3}}} d x

s im pl i f y - arcsin (\frac{1}{4} x) + \frac{x}{16 - x ^{2}} + C

\int (x + 1) x^{2} + 2 x + 2 d x

\int \frac{1}{x ^{2}} sin^{2} (\frac{1}{x}) d x

\int_{- 2}^{4} x - 9 d x