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

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

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

The first derivative of (x*cos(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 \cdot 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}}

\int 163 cos^{4} (3 x) sin^{2} (3 x) d x

\int 5^{- 4 (x - 7)} d x

\frac{d}{d x} (\frac{6}{3 x})

\frac{d}{d x} (6 x - x^{2})

\frac{\partial}{\partial x} (x^{3} y^{1} 0 sin (x y^{2}))

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