What is the derivative of sqrt(cos(3x)) ?

The derivative of sqrt(cos(3x)) is -(3sin(3x))/(2sqrt(cos(3x)))

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

The first derivative of sqrt(cos(3x)) is -(3sin(3x))/(2sqrt(cos(3x)))

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

- \frac{3 sin ( 3 x )}{2 cos ( 3 x )}

Solution steps

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

Apply the chain rule:

\frac{1}{2 cos ( 3 x )} \frac{d}{d x} (cos (3 x))

= \frac{1}{2 cos ( 3 x )} \frac{d}{d x} (cos (3 x))

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

= \frac{1}{2 cos ( 3 x )} (- sin (3 x) \cdot 3)

Simplify

\frac{1}{2 cos ( 3 x )} (- sin (3 x) \cdot 3) : - \frac{3 sin ( 3 x )}{2 cos ( 3 x )}

= - \frac{3 sin ( 3 x )}{2 cos ( 3 x )}

What is the derivative of sqrt(cos(3x)) ?
The derivative of sqrt(cos(3x)) is -(3sin(3x))/(2sqrt(cos(3x)))
What is the first derivative of sqrt(cos(3x)) ?
The first derivative of sqrt(cos(3x)) is -(3sin(3x))/(2sqrt(cos(3x)))