What is (\partial)/(\partial y)(3x+x^2y) ?

The answer to (\partial)/(\partial y)(3x+x^2y) is x^2

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(\partial)/(\partial y)(3x+x^2y)

\frac{\partial}{\partial y} (3 x + x^{2} y)

x^{2}

Solution steps

\frac{\partial}{\partial y} (3 x + x^{2} y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (3 x) + \frac{\partial}{\partial y} (x^{2} y)

\frac{\partial}{\partial y} (3 x) = 0

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

= 0 + x^{2}

Simplify

= x^{2}

x \to 1 lim ((a x^{2} - b x)^{2})

\frac{d}{d x} (2 c e^{2 x})

\frac{d y}{d x} = \frac{( 2 x ( y - 2 ) )}{x ^{2} + 1}, y (0) = 4

t \to 0 lim (e^{- t})

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

What is (\partial)/(\partial y)(3x+x^2y) ?
The answer to (\partial)/(\partial y)(3x+x^2y) is x^2