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

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

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

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

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

sin (3 x)

Solution steps

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

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