What is the derivative of sqrt((1+cos(x)/2)) ?

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{1 + c o s ( x )}{2}} (- \frac{1}{2} sin (x))

Simplify

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

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

\int e^{x} sin (6 x) d x

\frac{d}{d x} (\frac{x ^{3} + 2}{3})

\int e^{6 x} cos (2 x) d x

\frac{d}{d x} (\frac{4}{4 x})

y^{^{''}} + 2 y^{^{'}} + 1 y = 0

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