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Beliebt Rechnen >

derivative of sin(2xcos(x))

Lösung

\frac{d}{d x} (sin (2 x) cos (x))

Lösung

2 cos (2 x) cos (x) - sin (x) sin (2 x)

Schritte zur Lösung

\frac{d}{d x} (sin (2 x) cos (x))

Wende die Produktregel an:

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

f = sin (2 x), g = cos (x)

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

= cos (2 x) \cdot 2 cos (x) + (- sin (x)) sin (2 x)

Vereinfache

= 2 cos (2 x) cos (x) - sin (x) sin (2 x)

Graph

Beliebte Beispiele

(d^4)/(dx^4)(3e^{x^2})

\frac{d ^{4}}{d x ^{4}} (3 e^{x^{2}})

4y^{''}-4y^'+y=0

4 y^{^{''}} - 4 y^{^{'}} + y = 0

sum from n=1 to infinity of ln(1/(n^2))

n = 1 \sum \infty ln (\frac{1}{n ^{2}})

limit as x approaches 3 of (x^2-1)/(x-3)

x \to 3 lim (\frac{x ^{2} - 1}{x - 3})

\frac{d v}{d t}