What is the derivative of sqrt(cos(5x)) ?

The derivative of sqrt(cos(5x)) is -(5sin(5x))/(2sqrt(cos(5x)))

What is the first derivative of sqrt(cos(5x)) ?

The first derivative of sqrt(cos(5x)) is -(5sin(5x))/(2sqrt(cos(5x)))

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\frac{d}{d x} (cos (5 x))

- \frac{5 sin ( 5 x )}{2 cos ( 5 x )}

Solution steps

\frac{d}{d x} (cos (5 x))

Apply the chain rule:

\frac{1}{2 cos ( 5 x )} \frac{d}{d x} (cos (5 x))

= \frac{1}{2 cos ( 5 x )} \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= \frac{1}{2 cos ( 5 x )} (- sin (5 x) \cdot 5)

Simplify

\frac{1}{2 cos ( 5 x )} (- sin (5 x) \cdot 5) : - \frac{5 sin ( 5 x )}{2 cos ( 5 x )}

= - \frac{5 sin ( 5 x )}{2 cos ( 5 x )}

What is the derivative of sqrt(cos(5x)) ?
The derivative of sqrt(cos(5x)) is -(5sin(5x))/(2sqrt(cos(5x)))
What is the first derivative of sqrt(cos(5x)) ?
The first derivative of sqrt(cos(5x)) is -(5sin(5x))/(2sqrt(cos(5x)))