What is the derivative of xcos(6x) ?

The derivative of xcos(6x) is cos(6x)-6xsin(6x)

What is the first derivative of xcos(6x) ?

The first derivative of xcos(6x) is cos(6x)-6xsin(6x)

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

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

Solution steps

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

Apply the Product Rule:

(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

Simplify

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

y = \frac{2 ( 2 x ^{5} - 9 )}{x ^{4}}

\int csc^{3} (x) sec (x) d x

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

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

f (x) = - x^{2} + 25, at x = 3

What is the derivative of xcos(6x) ?
The derivative of xcos(6x) is cos(6x)-6xsin(6x)
What is the first derivative of xcos(6x) ?
The first derivative of xcos(6x) is cos(6x)-6xsin(6x)