What is (\partial)/(\partial x)((-cos(x))/(sqrt(x))) ?

The answer to (\partial)/(\partial x)((-cos(x))/(sqrt(x))) is -(-2xsin(x)-cos(x))/(2xsqrt(x))

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(\partial)/(\partial x)((-cos(x))/(sqrt(x)))

\frac{\partial}{\partial x} (\frac{- cos ( x )}{x})

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

Solution steps

\frac{\partial}{\partial x} (\frac{- cos ( x )}{x})

Simplify

\frac{- cos ( x )}{x} : - \frac{cos ( x )}{x}

= \frac{\partial}{\partial x} (- \frac{cos ( x )}{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{\partial}{\partial x} (\frac{cos ( x )}{x})

Apply the Quotient Rule:

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

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

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

\frac{\partial}{\partial 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 (\partial)/(\partial x)((-cos(x))/(sqrt(x))) ?
The answer to (\partial)/(\partial x)((-cos(x))/(sqrt(x))) is -(-2xsin(x)-cos(x))/(2xsqrt(x))