What is (\partial)/(\partial y)((2x+3y)^{10}) ?

The answer to (\partial)/(\partial y)((2x+3y)^{10}) is 30(2x+3y)^9

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(\partial)/(\partial y)((2x+3y)^{10})

\frac{\partial}{\partial y} ((2 x + 3 y)^{10})

30 (2 x + 3 y)^{9}

Solution steps

\frac{\partial}{\partial y} ((2 x + 3 y)^{10})

Treat

x

as a constant

Apply the chain rule:

10 (2 x + 3 y)^{9} \frac{\partial}{\partial y} (2 x + 3 y)

= 10 (2 x + 3 y)^{9} \frac{\partial}{\partial y} (2 x + 3 y)

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

= 10 (2 x + 3 y)^{9} \cdot 3

Simplify

= 30 (2 x + 3 y)^{9}

What is (\partial)/(\partial y)((2x+3y)^{10}) ?
The answer to (\partial)/(\partial y)((2x+3y)^{10}) is 30(2x+3y)^9