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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derivative of

\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}}

\frac{x ^{2}}{( e ^{x} - 1 )}

2 cos (2 x - 1)

x^{2} x

\frac{cot ( x )}{2}

(e^{x})^{- 1}

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)