What is the derivative of 3xcos(3x) ?

The derivative of 3xcos(3x) is 3(cos(3x)-3xsin(3x))

What is the first derivative of 3xcos(3x) ?

The first derivative of 3xcos(3x) is 3(cos(3x)-3xsin(3x))

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\frac{d}{d x} (3 x cos (3 x))

3 (cos (3 x) - 3 x sin (3 x))

Solution steps

\frac{d}{d x} (3 x cos (3 x))

Take the constant out:

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

= 3 \frac{d}{d x} (x cos (3 x))

Apply the Product Rule:

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

f = x, g = cos (3 x)

= 3 (\frac{d x}{d x} cos (3 x) + \frac{d}{d x} (cos (3 x)) x)

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

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= 3 (1 \cdot cos (3 x) + (- sin (3 x) \cdot 3) x)

Simplify

= 3 (cos (3 x) - 3 x sin (3 x))

What is the derivative of 3xcos(3x) ?
The derivative of 3xcos(3x) is 3(cos(3x)-3xsin(3x))
What is the first derivative of 3xcos(3x) ?
The first derivative of 3xcos(3x) is 3(cos(3x)-3xsin(3x))