What is the derivative of sqrt(sin(\sqrt{x)}) ?

The derivative of sqrt(sin(\sqrt{x)}) is (cos(sqrt(x)))/(4sqrt(x)\sqrt{sin(\sqrt{x))}}

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

The first derivative of sqrt(sin(\sqrt{x)}) is (cos(sqrt(x)))/(4sqrt(x)\sqrt{sin(\sqrt{x))}}

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

\frac{cos ( x )}{4 x 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)) = \frac{cos ( x )}{2 x}

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

Simplify

\frac{1}{2 sin ( x )} \cdot \frac{cos ( x )}{2 x} : \frac{cos ( x )}{4 x sin ( x )}

= \frac{cos ( x )}{4 x sin ( x )}

What is the derivative of sqrt(sin(\sqrt{x)}) ?
The derivative of sqrt(sin(\sqrt{x)}) is (cos(sqrt(x)))/(4sqrt(x)\sqrt{sin(\sqrt{x))}}
What is the first derivative of sqrt(sin(\sqrt{x)}) ?
The first derivative of sqrt(sin(\sqrt{x)}) is (cos(sqrt(x)))/(4sqrt(x)\sqrt{sin(\sqrt{x))}}