What is (\partial)/(\partial x)((3y)/(2x)) ?

The answer to (\partial)/(\partial x)((3y)/(2x)) is -(3y)/(2x^2)

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(\partial)/(\partial x)((3y)/(2x))

\frac{\partial}{\partial x} (\frac{3 y}{2 x})

- \frac{3 y}{2 x ^{2}}

Solution steps

\frac{\partial}{\partial x} (\frac{3 y}{2 x})

Treat

y

as a constant

Take the constant out:

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

= \frac{3 y}{2} \frac{\partial}{\partial x} (\frac{1}{x})

Apply exponent rule:

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

= \frac{3 y}{2} \frac{\partial}{\partial x} (x^{- 1})

Apply the Power Rule:

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

= \frac{3 y}{2} (- 1 \cdot x^{- 1 - 1})

Simplify

\frac{3 y}{2} (- 1 \cdot x^{- 1 - 1}) : - \frac{3 y}{2 x ^{2}}

= - \frac{3 y}{2 x ^{2}}

f (x) = \frac{x ^{2}}{7 + x}

x y^{^{'}} - 2 y = 2 y x^{2}

\frac{d}{d x} ((x^{2} - 3 x)^{6} (4 - x)^{5})

x \to 2 lim (e^{\frac{1}{x - 2}})

x \to 0 lim (x \cdot cot (2 x))

What is (\partial)/(\partial x)((3y)/(2x)) ?
The answer to (\partial)/(\partial x)((3y)/(2x)) is -(3y)/(2x^2)