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})

Simplify

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

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

Take the constant out:

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

= - \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}

\int \frac{5 x e ^{2 x}}{( 1 + 2 x ) ^{2}} d x

\int sin^{5} (3 x) cos^{3} (3 x) d x

\frac{d}{d x} (arctan (- 4 x))

f (x) = \frac{x ^{2} + 1}{2 x - 3}

\frac{d}{d x} (\frac{x ^{2}}{1 - 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))