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

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

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

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

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derivative of

sin (x)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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