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Popular >

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}}

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3 x^{5} x + \frac{7}{x ^{3} x}

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

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

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\frac{6}{s ^{2} + 5 s + 4}

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\frac{d}{d x} (8 4 x^{2} + 7)

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)