What is (\partial)/(\partial y)(x(x+y)) ?

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

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(\partial)/(\partial y)(x(x+y))

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

x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= x (0 + 1)

Simplify

= x

x \to \infty lim (x (arctan (x) - \frac{π}{2}))

f (x) = (7 x^{6} + 8 x^{3})^{4}

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 5

x \to 0 + lim ((cot (x))^{s i n (x)})

\frac{d y}{d t} + 2 (t + 1) y^{2} = 0

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