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

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

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

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

5 (x + y)^{4}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= 5 (x + y)^{4} \cdot 1

Simplify

= 5 (x + y)^{4}

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