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

The derivative of (sin(x)/(sqrt(x))) is (2xcos(x)-sin(x))/(2xsqrt(x))

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

The first derivative of (sin(x)/(sqrt(x))) is (2xcos(x)-sin(x))/(2xsqrt(x))

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ( x ) ) x - \frac{d}{d x} ( x ) sin ( x )}{( x ) ^{2}}

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

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

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

Simplify

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

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

What is the derivative of (sin(x)/(sqrt(x))) ?
The derivative of (sin(x)/(sqrt(x))) is (2xcos(x)-sin(x))/(2xsqrt(x))
What is the first derivative of (sin(x)/(sqrt(x))) ?
The first derivative of (sin(x)/(sqrt(x))) is (2xcos(x)-sin(x))/(2xsqrt(x))