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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Simplify

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

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

\int_{- 1}^{1} - x^{2} + 1 d x

\frac{\partial}{\partial y} (x^{5} y^{10} cos (x y^{2}))

\frac{d}{d x} (∣ 2 x - 3 ∣)

\frac{d}{d x} (25 e^{5 x})

\frac{\partial}{\partial x} (\frac{31 x y}{x - y})

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