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

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

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

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

y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{2}) = 0

= y + 0

Simplify

= y

x^{3} + y^{3} - 9 x y = 0, (4, 2)

\int x e^{- x^{3}} d x

\int \frac{( 4 x ^{m} - 3 x ^{n} ) ^{3}}{x} d x

x \to \infty lim ((- 1)^{- x})

\int (x^{4} - x^{2} + \frac{1}{4 x ^{3}} - \frac{1}{x ^{2}}) d x

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