What is the derivative of (cos(x-1)/x) ?

The derivative of (cos(x-1)/x) is (-xsin(x)-cos(x)+1)/(x^2)

What is the first derivative of (cos(x-1)/x) ?

The first derivative of (cos(x-1)/x) is (-xsin(x)-cos(x)+1)/(x^2)

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\frac{d}{d x} (\frac{cos ( x ) - 1}{x})

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

Solution steps

\frac{d}{d x} (\frac{cos ( x ) - 1}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (cos (x) - 1) = - sin (x)

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

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

Simplify

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

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

What is the derivative of (cos(x-1)/x) ?
The derivative of (cos(x-1)/x) is (-xsin(x)-cos(x)+1)/(x^2)
What is the first derivative of (cos(x-1)/x) ?
The first derivative of (cos(x-1)/x) is (-xsin(x)-cos(x)+1)/(x^2)