What is (\partial)/(\partial y)(600-4x+10x^2y) ?

The answer to (\partial)/(\partial y)(600-4x+10x^2y) is 10x^2

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(\partial)/(\partial y)(600-4x+10x^2y)

\frac{\partial}{\partial y} (600 - 4 x + 10 x^{2} y)

10 x^{2}

Solution steps

\frac{\partial}{\partial y} (600 - 4 x + 10 x^{2} y)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (600) - \frac{\partial}{\partial y} (4 x) + \frac{\partial}{\partial y} (10 x^{2} y)

\frac{\partial}{\partial y} (600) = 0

\frac{\partial}{\partial y} (4 x) = 0

\frac{\partial}{\partial y} (10 x^{2} y) = 10 x^{2}

= 0 - 0 + 10 x^{2}

Simplify

= 10 x^{2}

\int (4 x + 1)^{\frac{1}{2}} d x

\int_{\frac{1}{2}}^{2} \frac{2}{x} - \frac{1}{2} x d x

\int \frac{4 - 32 x}{81 - 16 x ^{2}} d x

x \to 3 lim (\frac{9 + x}{3 - x})

x \to \infty lim (8 x + 5)

What is (\partial)/(\partial y)(600-4x+10x^2y) ?
The answer to (\partial)/(\partial y)(600-4x+10x^2y) is 10x^2