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

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

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

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

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

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

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 x}{d x} cos ( x )}{x ^{2}}

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

\frac{d x}{d x} = 1

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

Simplify

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

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

(2 x y^{2} - 3) d x + (2 x^{2} y + 4) d y = 0

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

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 8)^{9})

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

(3)^{x}

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