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

The answer to (\partial)/(\partial y)(2y^2sqrt(x)) is 4ysqrt(x)

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

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

4 y x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 4 y x

What is (\partial)/(\partial y)(2y^2sqrt(x)) ?
The answer to (\partial)/(\partial y)(2y^2sqrt(x)) is 4ysqrt(x)