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

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

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

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

2 (y + 3) (x + 2)

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

2 (x + 2) \frac{\partial}{\partial x} (x + 2)

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

\frac{\partial}{\partial x} (x + 2) = 1

= (y + 3) \cdot 2 (x + 2) \cdot 1

Simplify

= 2 (y + 3) (x + 2)

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