What is the derivative of (xcos(pix+1)/(1-x)) ?

The derivative of (xcos(pix+1)/(1-x)) is (-pixsin(pix)+pix^2sin(pix)+cos(pix)+1)/((1-x)^2)

What is the first derivative of (xcos(pix+1)/(1-x)) ?

The first derivative of (xcos(pix+1)/(1-x)) is (-pixsin(pix)+pix^2sin(pix)+cos(pix)+1)/((1-x)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{s + 1}{s ^{2} + 2}

(y - x 2) d x + (x + y 2) d y = 0

\int (\frac{- 4}{x}) d x

\int \frac{1}{n} sin (n x) d x

\frac{104}{s ^{2} + 8 s + 52}

What is the derivative of (xcos(pix+1)/(1-x)) ?
The derivative of (xcos(pix+1)/(1-x)) is (-pixsin(pix)+pix^2sin(pix)+cos(pix)+1)/((1-x)^2)
What is the first derivative of (xcos(pix+1)/(1-x)) ?
The first derivative of (xcos(pix+1)/(1-x)) is (-pixsin(pix)+pix^2sin(pix)+cos(pix)+1)/((1-x)^2)