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

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

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

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

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

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

Solution steps

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

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

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

\frac{d}{d x} (π - x) = - 1

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

Simplify

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

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

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