What is (\partial)/(\partial y)(5/y) ?

The answer to (\partial)/(\partial y)(5/y) is -5/(y^2)

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(\partial)/(\partial y)(5/y)

\frac{\partial}{\partial y} (\frac{5}{y})

- \frac{5}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{5}{y})

Take the constant out:

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

= 5 \frac{\partial}{\partial y} (\frac{1}{y})

Apply exponent rule:

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

= 5 \frac{\partial}{\partial y} (y^{- 1})

Apply the Power Rule:

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

= 5 (- 1 \cdot y^{- 1 - 1})

Simplify

5 (- 1 \cdot y^{- 1 - 1}) : - \frac{5}{y ^{2}}

= - \frac{5}{y ^{2}}

What is (\partial)/(\partial y)(5/y) ?
The answer to (\partial)/(\partial y)(5/y) is -5/(y^2)