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

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

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

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

2 y x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 y x

\int \frac{1}{1 + 2 u} d u

\int (3 x^{2} - 4 x + 7) d x

f (x) = (\frac{x ^{2} + 4}{x ^{2} - 4})^{4}

\frac{d y}{d x} = \frac{( x y + 3 x - y - 3 )}{( x y - 2 x + 4 y - 8 )}

\int x^{2} + 6 x^{- \frac{3}{2}} d x

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