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

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

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

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

\frac{2}{y ^{3}}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (2) = 0

= \frac{1}{y ^{3}} (2 + 0)

Simplify

\frac{1}{y ^{3}} (2 + 0) : \frac{2}{y ^{3}}

= \frac{2}{y ^{3}}

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