What is the derivative of (xcos(x-2pi)/(x-2pi)) ?

The derivative of (xcos(x-2pi)/(x-2pi)) is (-x^2sin(x)+2pixsin(x)-2picos(x)+2pi)/((x-2pi)^2)

What is the first derivative of (xcos(x-2pi)/(x-2pi)) ?

The first derivative of (xcos(x-2pi)/(x-2pi)) is (-x^2sin(x)+2pixsin(x)-2picos(x)+2pi)/((x-2pi)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (x - 2 π) = 1

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

Simplify

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

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

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

\frac{d}{d x} ((3 x^{2} + 1)^{4})

k = 1 \sum \infty \frac{k ^{3}}{3 ^{k}}

y^{^{'}} + 3 y = 2 e^{- 3 x}

y = x^{3} - x, (- 1, 0)

What is the derivative of (xcos(x-2pi)/(x-2pi)) ?
The derivative of (xcos(x-2pi)/(x-2pi)) is (-x^2sin(x)+2pixsin(x)-2picos(x)+2pi)/((x-2pi)^2)
What is the first derivative of (xcos(x-2pi)/(x-2pi)) ?
The first derivative of (xcos(x-2pi)/(x-2pi)) is (-x^2sin(x)+2pixsin(x)-2picos(x)+2pi)/((x-2pi)^2)