What is (\partial)/(\partial y)((x-y)^5) ?

The answer to (\partial)/(\partial y)((x-y)^5) is -5(x-y)^4

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(\partial)/(\partial y)((x-y)^5)

\frac{\partial}{\partial y} ((x - y)^{5})

- 5 (x - y)^{4}

Solution steps

\frac{\partial}{\partial y} ((x - y)^{5})

Treat

x

as a constant

Apply the chain rule:

5 (x - y)^{4} \frac{\partial}{\partial y} (x - y)

= 5 (x - y)^{4} \frac{\partial}{\partial y} (x - y)

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

= 5 (x - y)^{4} (- 1)

Simplify

= - 5 (x - y)^{4}

What is (\partial)/(\partial y)((x-y)^5) ?
The answer to (\partial)/(\partial y)((x-y)^5) is -5(x-y)^4