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

The derivative of (cos(x)/(sqrt(x))) is (-2xsin(x)-cos(x))/(2xsqrt(x))

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

The first derivative of (cos(x)/(sqrt(x))) is (-2xsin(x)-cos(x))/(2xsqrt(x))

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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