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Beliebt Rechnen >

(xsin(2pix))^'

Lösung

(x sin (2 π x))^{^{'}}

Lösung

sin (2 π x) + 2 π x cos (2 π x)

Schritte zur Lösung

(x sin (2 π x))^{'}

Wende die Produktregel an:

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

f = x, g = sin (2 π x)

= x^{^{'}} sin (2 π x) + (sin (2 π x))^{^{'}} x

x^{'} = 1

(sin (2 π x))^{'} = cos (2 π x) \cdot 2 π

= 1 \cdot sin (2 π x) + cos (2 π x) \cdot 2 π x

Vereinfache

= sin (2 π x) + 2 π x cos (2 π x)

Graph

Beliebte Beispiele

integral from 0 to 1 of pi(x-x^4)^2

\int_{0}^{1} π (x - x^{4})^{2} d x

laplacetransform e^{t+7}

l a pl a ce t r an s f or m e^{t + 7}

integral of 5xsqrt(1-x^4)

\int 5 x 1 - x^{4} d x

derivative x(x^2+4)^5

d er i v a t i v e x (x^{2} + 4)^{5}

derivative f(x)=5x+2x^2+7e^x

d er i v a t i v e f (x) = 5 x + 2 x^{2} + 7 e^{x}