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

The answer to (\partial)/(\partial x)((2x+3y)^{10}) is 20(2x+3y)^9

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

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

20 (2 x + 3 y)^{9}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 20 (2 x + 3 y)^{9}

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What is (\partial)/(\partial x)((2x+3y)^{10}) ?
The answer to (\partial)/(\partial x)((2x+3y)^{10}) is 20(2x+3y)^9