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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

Solution steps

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

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

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

\frac{d}{d x} (x - 2) = 1

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

Simplify

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

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

\frac{\partial ^{2}}{\partial y \partial x} (x y e^{- 6 y})

y^{^{'}} - y = 7

\frac{\partial}{\partial u} (sin (u))

f (x) = \frac{c ^{5} - x ^{5}}{c ^{5} + c ^{5}}, c

3 + 5 sin (s)

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