What is (\partial)/(\partial x)((9x+2y)^5) ?

The answer to (\partial)/(\partial x)((9x+2y)^5) is 45(9x+2y)^4

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(\partial)/(\partial x)((9x+2y)^5)

\frac{\partial}{\partial x} ((9 x + 2 y)^{5})

45 (9 x + 2 y)^{4}

Solution steps

\frac{\partial}{\partial x} ((9 x + 2 y)^{5})

Treat

y

as a constant

Apply the chain rule:

5 (9 x + 2 y)^{4} \frac{\partial}{\partial x} (9 x + 2 y)

= 5 (9 x + 2 y)^{4} \frac{\partial}{\partial x} (9 x + 2 y)

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

= 5 (9 x + 2 y)^{4} \cdot 9

Simplify

= 45 (9 x + 2 y)^{4}

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What is (\partial)/(\partial x)((9x+2y)^5) ?
The answer to (\partial)/(\partial x)((9x+2y)^5) is 45(9x+2y)^4