derivative of 4xsin(pix)

Lösung

\frac{d}{d x} (4 x sin (π x))

4 (sin (π x) + π x cos (π x))

Schritte zur Lösung

\frac{d}{d x} (4 x sin (π x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (x sin (π x))

Wende die Produktregel an:

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

f = x, g = sin (π x)

= 4 (\frac{d x}{d x} sin (π x) + \frac{d}{d x} (sin (π x)) x)

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

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

= 4 (1 \cdot sin (π x) + cos (π x) π x)

Vereinfache

= 4 (sin (π x) + π x cos (π x))

t an g e n t f (x) = \frac{x ^{2}}{x + 8}, at x = 2

\int 10 x ln (9 x) d x

\int_{- π}^{0} sin (x) d x

\frac{d}{d x} (\frac{( x ^{2} )}{x - 1})

x \to 0 lim (\frac{x ^{2} - 4 x}{x})