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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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