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

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

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

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

y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= y (1 + 0)

Simplify

= y

(y sin (x) + x y cos (x)) d x + (x sin (x) + 1) d y

(x - h)^{2} + (y - k)^{2}

(cos (x) - sin (x) - 1)^{2}

\frac{1}{s ( s + 5 ) ^{3}}

2 x (2 x + 1)

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