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Beliebt Rechnen >

derivative of 8x*sin(x)

Lösung

\frac{d}{d x} (8 x \cdot sin (x))

Lösung

8 (sin (x) + x cos (x))

Schritte zur Lösung

\frac{d}{d x} (8 x sin (x))

Entferne die Konstante:

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

= 8 \frac{d}{d x} (x sin (x))

Wende die Produktregel an:

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

f = x, g = sin (x)

= 8 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

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

= 8 (1 \cdot sin (x) + cos (x) x)

Vereinfache

= 8 (sin (x) + x cos (x))

Graph

Beliebte Beispiele

integral of 1/pi sin(pix)

\int \frac{1}{π} sin (π x) d x

derivative y=\sqrt[4]{x}

d er i v a t i v e y = 4 x

derivative y=(sqrt(x))/(8+x)

d er i v a t i v e y = \frac{x}{8 + x}

derivative of cot^7(x)

\frac{d}{d x} (cot^{7} (x))

2yy^'+2=y^2+2x,y(0)=4

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 4