What is the derivative of ((x-2/(x-pi))^{-3}) ?

The derivative of ((x-2/(x-pi))^{-3}) is -(3(-pi+2)(x-pi)^2)/((x-2)^4)

What is the first derivative of ((x-2/(x-pi))^{-3}) ?

The first derivative of ((x-2/(x-pi))^{-3}) is -(3(-pi+2)(x-pi)^2)/((x-2)^4)

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\frac{d}{d x} ((\frac{x - 2}{x - π})^{- 3})

- \frac{3 ( - π + 2 ) ( x - π ) ^{2}}{( x - 2 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{x - 2}{x - π})^{- 3})

Apply the chain rule:

- \frac{3}{( \frac{x - 2}{x - π} ) ^{4}} \frac{d}{d x} (\frac{x - 2}{x - π})

= - \frac{3}{( \frac{x - 2}{x - π} ) ^{4}} \frac{d}{d x} (\frac{x - 2}{x - π})

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

= - \frac{3}{( \frac{x - 2}{x - π} ) ^{4}} \cdot \frac{- π + 2}{( x - π ) ^{2}}

Simplify

- \frac{3}{( \frac{x - 2}{x - π} ) ^{4}} \cdot \frac{- π + 2}{( x - π ) ^{2}} : - \frac{3 ( - π + 2 ) ( x - π ) ^{2}}{( x - 2 ) ^{4}}

= - \frac{3 ( - π + 2 ) ( x - π ) ^{2}}{( x - 2 ) ^{4}}

What is the derivative of ((x-2/(x-pi))^{-3}) ?
The derivative of ((x-2/(x-pi))^{-3}) is -(3(-pi+2)(x-pi)^2)/((x-2)^4)
What is the first derivative of ((x-2/(x-pi))^{-3}) ?
The first derivative of ((x-2/(x-pi))^{-3}) is -(3(-pi+2)(x-pi)^2)/((x-2)^4)