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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

x \to 2 lim (\frac{( x - 2 )}{x})

(((- 3)^{^{'}})^{4})^{^{'}}

\frac{d}{d x} (\frac{x ^{4} + 7 x ^{3} + 14 x ^{2}}{x + 3})

\int 3 y^{2} d y

x \to 6 + lim (\frac{- 5 x}{x + 6})

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