What is (\partial)/(\partial x)(5x+10y+10xy) ?

The answer to (\partial)/(\partial x)(5x+10y+10xy) is 10y+5

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(\partial)/(\partial x)(5x+10y+10xy)

\frac{\partial}{\partial x} (5 x + 10 y + 10 x y)

10 y + 5

Solution steps

\frac{\partial}{\partial x} (5 x + 10 y + 10 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (10 y) + \frac{\partial}{\partial x} (10 x y)

\frac{\partial}{\partial x} (5 x) = 5

\frac{\partial}{\partial x} (10 y) = 0

\frac{\partial}{\partial x} (10 x y) = 10 y

= 5 + 0 + 10 y

Simplify

= 10 y + 5

What is (\partial)/(\partial x)(5x+10y+10xy) ?
The answer to (\partial)/(\partial x)(5x+10y+10xy) is 10y+5