What is (\partial}{\partial y}(\frac{4x)/y) ?

The answer to (\partial}{\partial y}(\frac{4x)/y) is -(4x)/(y^2)

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(\partial}{\partial y}(\frac{4x)/y)

\frac{\partial}{\partial y} (\frac{4 x}{y})

- \frac{4 x}{y ^{2}}

Solution steps

\frac{\partial}{\partial y} (\frac{4 x}{y})

Treat

x

as a constant

Take the constant out:

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

= 4 x \frac{\partial}{\partial y} (\frac{1}{y})

Apply exponent rule:

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

= 4 x \frac{\partial}{\partial y} (y^{- 1})

Apply the Power Rule:

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

= 4 x (- 1 \cdot y^{- 1 - 1})

Simplify

4 x (- 1 \cdot y^{- 1 - 1}) : - \frac{4 x}{y ^{2}}

= - \frac{4 x}{y ^{2}}

\frac{d}{d x} (- \frac{1}{2} x^{4})

x \to 4 lim (3 x^{3})

\int x^{2} cos (\frac{1}{4} x) d x

(16, 1.2), (32, 2.4)

n = 2 \sum \infty \frac{3}{n ( n + 2 )}

What is (\partial}{\partial y}(\frac{4x)/y) ?
The answer to (\partial}{\partial y}(\frac{4x)/y) is -(4x)/(y^2)