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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

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

y^{^{''}} + 4 y = 0

\int x sin (1 - 2 x) d x

\int \frac{2 - x}{x ^{2} - 2 x + 1} d x

x^{3}, x

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