What is (\partial)/(\partial y)((x+y)^8) ?

The answer to (\partial)/(\partial y)((x+y)^8) is 8(x+y)^7

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(\partial)/(\partial y)((x+y)^8)

\frac{\partial}{\partial y} ((x + y)^{8})

8 (x + y)^{7}

Solution steps

\frac{\partial}{\partial y} ((x + y)^{8})

Treat

x

as a constant

Apply the chain rule:

8 (x + y)^{7} \frac{\partial}{\partial y} (x + y)

= 8 (x + y)^{7} \frac{\partial}{\partial y} (x + y)

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

= 8 (x + y)^{7} \cdot 1

Simplify

= 8 (x + y)^{7}

\frac{\partial}{\partial y} (x^{2} y + y^{3})

x \to 2 lim (x^{2} + x - 2)

\int_{0}^{1} r^{3} d r

\frac{\partial}{\partial x} ((x^{2} + y^{2}) e^{x^{2} y})

\frac{x}{( x ^{2} - 1 )}

What is (\partial)/(\partial y)((x+y)^8) ?
The answer to (\partial)/(\partial y)((x+y)^8) is 8(x+y)^7