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Beliebt Rechnen >

derivative of xsin(pix)

Lösung

\frac{d}{d x} (x sin (π x))

Lösung

sin (π x) + π x cos (π x)

Schritte zur Lösung

\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)

= \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

= 1 \cdot sin (π x) + cos (π x) π x

Vereinfache

= sin (π x) + π x cos (π x)

Graph

Beliebte Beispiele

derivative of 9e^x(cos(x-sin(x)))

\frac{d}{d x} (9 e^{x} (cos (x) - sin (x)))

integral of (cos(x)+5^x)

\int (cos (x) + 5^{x}) d x

integral of (x^2+6x)cos(x)

\int (x^{2} + 6 x) cos (x) d x

derivative of e^{ax^6}

\frac{d}{d x} (e^{a x^{6}})

derivative f(x)=(x)^3*e^{(3x)}

d er i v a t i v e f (x) = (x)^{3} \cdot e^{(3 x)}