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

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

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

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

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

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

Solution steps

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

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

\frac{d}{d x} (x - π) = 1

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

Simplify

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

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

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