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

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

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

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

\frac{5}{( x + 2 ) ^{2}}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (y) = 1

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

= \frac{5}{( x + 2 ) ^{2}} (1 + 0)

Simplify

= \frac{5}{( x + 2 ) ^{2}}

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