What is (\partial)/(\partial y)((2x+3y)^7) ?

The answer to (\partial)/(\partial y)((2x+3y)^7) is 21(2x+3y)^6

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(\partial)/(\partial y)((2x+3y)^7)

\frac{\partial}{\partial y} ((2 x + 3 y)^{7})

21 (2 x + 3 y)^{6}

Solution steps

\frac{\partial}{\partial y} ((2 x + 3 y)^{7})

Treat

x

as a constant

Apply the chain rule:

7 (2 x + 3 y)^{6} \frac{\partial}{\partial y} (2 x + 3 y)

= 7 (2 x + 3 y)^{6} \frac{\partial}{\partial y} (2 x + 3 y)

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

= 7 (2 x + 3 y)^{6} \cdot 3

Simplify

= 21 (2 x + 3 y)^{6}

What is (\partial)/(\partial y)((2x+3y)^7) ?
The answer to (\partial)/(\partial y)((2x+3y)^7) is 21(2x+3y)^6