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}

\frac{d}{d x} (\frac{5 ^{x}}{ln ( 5 )})

\int (e - x - e^{2}) (e x + e - 5) d x

\int 3 e^{3 x} d x

\frac{d}{d x} (\frac{3}{x + 3})

2 x - 3 y x^{2} + 1 \frac{d y}{d x} = 0

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