What is the derivative of 1/3 cos(3x) ?

The derivative of 1/3 cos(3x) is -sin(3x)

What is the first derivative of 1/3 cos(3x) ?

The first derivative of 1/3 cos(3x) is -sin(3x)

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\frac{d}{d x} (\frac{1}{3} cos (3 x))

- sin (3 x)

Solution steps

\frac{d}{d x} (\frac{1}{3} cos (3 x))

Take the constant out:

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

= \frac{1}{3} \frac{d}{d x} (cos (3 x))

Apply the chain rule:

- sin (3 x) \frac{d}{d x} (3 x)

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

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

= \frac{1}{3} (- sin (3 x) \cdot 3)

Simplify

\frac{1}{3} (- sin (3 x) \cdot 3) : - sin (3 x)

= - sin (3 x)

What is the derivative of 1/3 cos(3x) ?
The derivative of 1/3 cos(3x) is -sin(3x)
What is the first derivative of 1/3 cos(3x) ?
The first derivative of 1/3 cos(3x) is -sin(3x)