What is the derivative of (cos(sqrt(x))/(2sqrt(x))) ?

The derivative of (cos(sqrt(x))/(2sqrt(x))) is (-sqrt(x)sin(sqrt(x))-cos(sqrt(x)))/(4xsqrt(x))

What is the first derivative of (cos(sqrt(x))/(2sqrt(x))) ?

The first derivative of (cos(sqrt(x))/(2sqrt(x))) is (-sqrt(x)sin(sqrt(x))-cos(sqrt(x)))/(4xsqrt(x))

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

\frac{- x sin ( x ) - cos ( x )}{4 x x}

Solution steps

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

Take the constant out:

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

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

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

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

= \frac{1}{2} \cdot \frac{( - \frac{s i n ( x )}{2 x} ) x - \frac{1}{2 x} cos ( x )}{( x ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( - \frac{s i n ( x )}{2 x} ) x - \frac{1}{2 x} cos ( x )}{( x ) ^{2}} : \frac{- x sin ( x ) - cos ( x )}{4 x x}

= \frac{- x sin ( x ) - cos ( x )}{4 x x}

f (x) = 9 - 3 x + 2 x^{2}, at x = - 6

\frac{d}{d x} (2 x - 3 x^{\frac{2}{3}})

\int 25 e^{- 2 x} d x

x \to 3 - lim (x - 2)

x \to \frac{π}{2} - lim (cot (2 x))

What is the derivative of (cos(sqrt(x))/(2sqrt(x))) ?
The derivative of (cos(sqrt(x))/(2sqrt(x))) is (-sqrt(x)sin(sqrt(x))-cos(sqrt(x)))/(4xsqrt(x))
What is the first derivative of (cos(sqrt(x))/(2sqrt(x))) ?
The first derivative of (cos(sqrt(x))/(2sqrt(x))) is (-sqrt(x)sin(sqrt(x))-cos(sqrt(x)))/(4xsqrt(x))