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Popular >

derivative of (cos(x)/x)

Solution

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

Solution

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

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

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

Simplify

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

Popular Examples

derivative of-3/4 x^{1/3}

\frac{d}{d x} (- \frac{3}{4} x^{\frac{1}{3}})

y^{^{'}} - \frac{3 y}{x} = x

derivative of sin(x^2)+((1-x))/(1+x)derivative of

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

(\partial)/(\partial x)(2/(x+2y))

\frac{\partial}{\partial x} (\frac{2}{x + 2 y})

derivative of ((x^2-1)/(x^2+x+1))

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

Frequently Asked Questions (FAQ)

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