What is (\partial)/(\partial x)((x+2)^2*(1+1/y)^3) ?

The answer to (\partial)/(\partial x)((x+2)^2*(1+1/y)^3) is 2(1+1/y)^3(x+2)

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(\partial)/(\partial x)((x+2)^2*(1+1/y)^3)

\frac{\partial}{\partial x} ((x + 2)^{2} \cdot (1 + \frac{1}{y})^{3})

2 (1 + \frac{1}{y})^{3} (x + 2)

Solution steps

\frac{\partial}{\partial x} ((x + 2)^{2} (1 + \frac{1}{y})^{3})

Treat

y

as a constant

Take the constant out:

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

= (1 + \frac{1}{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

= (1 + \frac{1}{y})^{3} \cdot 2 (x + 2) \cdot 1

Simplify

= 2 (1 + \frac{1}{y})^{3} (x + 2)

y = x^{2} + 11

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What is (\partial)/(\partial x)((x+2)^2*(1+1/y)^3) ?
The answer to (\partial)/(\partial x)((x+2)^2*(1+1/y)^3) is 2(1+1/y)^3(x+2)