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Popular >

derivative of (cos(x))/x

Solution

derivative of

\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}}

Graph

Popular Examples

integral of ((e^x-1)/(e^x+1))

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

derivative of sqrt(25+(12-x^2)+x)

\frac{d}{d x} (25 + (12 - x)^{2} + x)

integral of e^{iax}

\int e^{ia x} d x

integral of e^{e^t}

\int e^{e^{t}} d t

(\partial)/(\partial y)(x^2y+3xy+y^2)

\frac{\partial}{\partial y} (x^{2} y + 3 x y + y^{2})

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)