What is (\partial)/(\partial x)(x^2y+10xy) ?

The answer to (\partial)/(\partial x)(x^2y+10xy) is 2yx+10y

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(\partial)/(\partial x)(x^2y+10xy)

\frac{\partial}{\partial x} (x^{2} y + 10 x y)

2 y x + 10 y

Solution steps

\frac{\partial}{\partial x} (x^{2} y + 10 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (10 x y)

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

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

= 2 y x + 10 y

What is (\partial)/(\partial x)(x^2y+10xy) ?
The answer to (\partial)/(\partial x)(x^2y+10xy) is 2yx+10y