What is (\partial)/(\partial y)(sqrt(xy^2)) ?

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

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(\partial)/(\partial y)(sqrt(xy^2))

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

x

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x y ^{2}} \cdot 2 x y : x

= x

x \to 0 + lim (e^{- x})

\frac{\partial}{\partial x} ((x^{2} + 5 x y - 2 y)^{8})

e^{- 5 t} sin (7 t)

\frac{d}{d x} (arctan (2 x^{3}))

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