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

The derivative of sqrt(cos(3x-1)) is -(3sin(3x-1))/(2sqrt(cos(3x-1)))

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

The first derivative of sqrt(cos(3x-1)) is -(3sin(3x-1))/(2sqrt(cos(3x-1)))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sqrt(cos(3x-1)) ?
The derivative of sqrt(cos(3x-1)) is -(3sin(3x-1))/(2sqrt(cos(3x-1)))
What is the first derivative of sqrt(cos(3x-1)) ?
The first derivative of sqrt(cos(3x-1)) is -(3sin(3x-1))/(2sqrt(cos(3x-1)))