What is the d/(dy)((2x)/y) ?

The d/(dy)((2x)/y) is -(2x)/(y^2)

What is the first d/(dy)((2x)/y) ?

The first d/(dy)((2x)/y) is -(2x)/(y^2)

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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