What is (\partial)/(\partial y)(xsqrt(y)) ?

The answer to (\partial)/(\partial y)(xsqrt(y)) is x/(2sqrt(y))

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(\partial)/(\partial y)(xsqrt(y))

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

\frac{x}{2 y}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

= 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{x}{2 y}

d P - k P d t = 0

\int 7 sin (2 t) d t

f (x) = x^{2} - 4 x, g (x) = 0, x = 0, x = 4

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

\frac{y ^{^{'}} - e ^{- t} + 3}{y} = - 3, y (0) = 4

What is (\partial)/(\partial y)(xsqrt(y)) ?
The answer to (\partial)/(\partial y)(xsqrt(y)) is x/(2sqrt(y))