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

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

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(\partial)/(\partial x)(y/(sqrt(x)))

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

\int_{- π}^{π} cos (2 x) d x

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

\int \frac{21}{1 - cos ( 3 x )} d x

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

x \frac{d y}{d x} + 4 y = x^{3} - x

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