What is the derivative of (cos(4x)/x) ?

The derivative of (cos(4x)/x) is (-4xsin(4x)-cos(4x))/(x^2)

What is the first derivative of (cos(4x)/x) ?

The first derivative of (cos(4x)/x) is (-4xsin(4x)-cos(4x))/(x^2)

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\frac{d}{d x} (\frac{cos ( 4 x )}{x})

\frac{- 4 x sin ( 4 x ) - cos ( 4 x )}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{cos ( 4 x )}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( cos ( 4 x ) ) x - \frac{d x}{d x} cos ( 4 x )}{x ^{2}}

\frac{d}{d x} (cos (4 x)) = - sin (4 x) \cdot 4

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

= \frac{( - sin ( 4 x ) \cdot 4 ) x - 1 \cdot cos ( 4 x )}{x ^{2}}

Simplify

= \frac{- 4 x sin ( 4 x ) - cos ( 4 x )}{x ^{2}}

What is the derivative of (cos(4x)/x) ?
The derivative of (cos(4x)/x) is (-4xsin(4x)-cos(4x))/(x^2)
What is the first derivative of (cos(4x)/x) ?
The first derivative of (cos(4x)/x) is (-4xsin(4x)-cos(4x))/(x^2)