What is the derivative of 2/y ?

The derivative of 2/y is -2/(y^2)

What is the first derivative of 2/y ?

The first derivative of 2/y is -2/(y^2)

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derivative of

\frac{2}{y}

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

Solution steps

\frac{d}{d y} (\frac{2}{y})

Take the constant out:

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

= 2 \frac{d}{d y} (\frac{1}{y})

Apply exponent rule:

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

= 2 \frac{d}{d y} (y^{- 1})

Apply the Power Rule:

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

= 2 (- 1 \cdot y^{- 1 - 1})

Simplify

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

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

\int \frac{x ^{2} - 2}{2 x} d x

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\int_{1}^{e^{4}} x^{5} ln (x) d x