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

The answer to (\partial)/(\partial y)(x^2y+sqrt(y)) is x^2+1/(2sqrt(y))

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

\int_{0}^{u} v + x d v

(1 - t^{2}) y^{^{'}} - t^{2} y = (1 + t) \cdot (1 - t^{2})

3 x^{2} + y^{2} = 1, (\frac{1}{2}, \frac{- 1}{2})

y^{^{''}} - y^{^{'}} + 12 y = 0

\frac{d}{d x} (\frac{( e ^{x} )}{1 - e ^{- x}})

What is (\partial)/(\partial y)(x^2y+sqrt(y)) ?
The answer to (\partial)/(\partial y)(x^2y+sqrt(y)) is x^2+1/(2sqrt(y))