What is the first (pi/x)^' ?

The first (pi/x)^' is -pi/(x^2)

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(pi/x)^'

(\frac{π}{x})^{^{'}}

- \frac{π}{x ^{2}}

Solution steps

(\frac{π}{x})^{'}

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= π (\frac{1}{x})^{^{'}}

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= π (x^{- 1})^{^{'}}

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= π (- 1 \cdot x^{- 1 - 1})

Simplify

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

= - \frac{π}{x ^{2}}

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