derivative of xcos(6x)

Lösung

\frac{d}{d x} (x cos (6 x))

cos (6 x) - 6 x sin (6 x)

Schritte zur Lösung

\frac{d}{d x} (x cos (6 x))

Wende die Produktregel an:

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

f = x, g = cos (6 x)

= \frac{d x}{d x} cos (6 x) + \frac{d}{d x} (cos (6 x)) x

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

\frac{d}{d x} (cos (6 x)) = - sin (6 x) \cdot 6

= 1 \cdot cos (6 x) + (- sin (6 x) \cdot 6) x

Vereinfache

= cos (6 x) - 6 x sin (6 x)

d er i v a t i v e y = \frac{2 ( 2 x ^{5} - 9 )}{x ^{4}}

\frac{d y}{d t} = y^{3}

y^{^{''}} + 2 y^{^{'}} + 2 y = 5 cos (3 t) - 20 sin (3 t)

t an g e n t f (x) = - x^{2} + 25, at x = 3

\int (1 + 2 x)^{- 1} d x