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}

y = \frac{8}{x ^{2} + 4}, (2, 1)

\int_{1}^{2} \frac{1}{8} + \frac{3}{8} x d x

\frac{d}{d x} ((3 x^{4} - x + 1) (- x^{5} + 4))

y^{^{'}} + 2 y = 1, y (0) = \frac{5}{2}

\int x (2 x + 3)^{2} d x

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