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

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

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

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

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derivative

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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