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Popular Calculus >

derivative of (cos(2x)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

Graph

Popular Examples

(\partial)/(\partial x)(ln(((x+y))/(x-y)))

\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

derivative of ((6e^x)/(2e^x+1))

\frac{d}{d x} (\frac{( 6 e ^{x} )}{2 e ^{x} + 1})

integral of 1/(xsqrt(121x^2-121))

\int \frac{1}{x 121 x ^{2} - 121} d x

integral of y+x

\int y + x d x

(\partial)/(\partial x)(in(x+2y+3z))

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

Frequently Asked Questions (FAQ)

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