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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int_{- 32}^{18} \frac{1}{∣ 2 x ∣} d x

n = 1 \sum \infty (\frac{1}{2 ^{n}}) - 1

\frac{d}{d x} ((x^{3} - 2)^{2})

\int 1000 t e^{- 0.5 t} d t

y^{^{''}} - 4 y^{^{'}} + 4 y = 120 x^{2} e^{2 x}

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