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

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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int \frac{( 2 - x ) ^{7}}{x} d x

\frac{d}{d y} (e^{x} tan (y))

\frac{d x}{d t} = t - x

\frac{d}{d x} (3 cos^{3} (x))

\int (5 x - 2)^{7} d x