What is (\partial)/(\partial x)((xy)^{0.5}) ?

The answer to (\partial)/(\partial x)((xy)^{0.5}) is (0.5y^{1/2})/(x^{1/2)}

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(\partial)/(\partial x)((xy)^{0.5})

\frac{\partial}{\partial x} ((x y)^{0.5})

\frac{0.5 y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

Solution steps

\frac{\partial}{\partial x} ((x y)^{0.5})

Treat

y

as a constant

Apply the chain rule:

\frac{0.5}{( x y ) ^{0.5}} \frac{\partial}{\partial x} (x y)

= \frac{0.5}{( x y ) ^{0.5}} \frac{\partial}{\partial x} (x y)

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

= \frac{0.5}{( x y ) ^{0.5}} y

Simplify

\frac{0.5}{( x y ) ^{\frac{1}{2}}} y : \frac{0.5 y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

= \frac{0.5 y ^{\frac{1}{2}}}{x ^{\frac{1}{2}}}

y^{^{'}} + sin (t) y = - sin (t), y (0) = 3

80 t^{2}

f (x) = x^{2} (1 - x)^{2}, at x = 2

x \to 0 lim (\frac{( x - 1 ) ^{2} + 1}{x})

\frac{( s + 1 ) ^{2}}{( s - 1 ) ^{3}}

What is (\partial)/(\partial x)((xy)^{0.5}) ?
The answer to (\partial)/(\partial x)((xy)^{0.5}) is (0.5y^{1/2})/(x^{1/2)}