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

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

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

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

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derivative of

cos (x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{1}^{3} x + 2 d x

3 y^{^{'}} + 12 y = 4

\int \frac{2 arcsin ( x )}{1 - x ^{2}} d x

2 x^{2} - 2 x + C

\int \frac{5}{x ^{7}} d x

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