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

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

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

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

- 2 y

Solution steps

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

Treat

x

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + y, g = x - y

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

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

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

= 1 \cdot (x - y) + (- 1) (x + y)

Simplify

1 \cdot (x - y) + (- 1) (x + y) : - 2 y

= - 2 y

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