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Beliebt Rechnen >

derivative of x^2sin(pix)

Lösung

\frac{d}{d x} (x^{2} sin (π x))

Lösung

2 x sin (π x) + cos (π x) π x^{2}

Schritte zur Lösung

\frac{d}{d x} (x^{2} sin (π x))

Wende die Produktregel an:

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

f = x^{2}, g = sin (π x)

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

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

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

= 2 x sin (π x) + cos (π x) π x^{2}

Graph

Beliebte Beispiele

(dy)/(dx)=ysec^2(x)

\frac{d y}{d x} = y sec^{2} (x)

3 y^{^{''}} + 108 y = 0

integral of (x-3)(sqrt(x+3))

\int (x - 3) (x + 3) d x

derivative of-4cos^3(x)

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

limit as x approaches 3 of 4

x \to 3 lim (4)