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

\frac{d}{d x} (tan^{40} (sec (cos (x))))

\frac{d}{d x} (x^{e} + \frac{1}{x ^{10}})

- \frac{x}{8 y}

\frac{d ^{2}}{d x ^{2}} ((4 x^{2} + 8 x) cos (x))

\frac{a}{s ^{2} + a ^{2}}

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