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

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

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

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

2 x + y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (5 y) = 0

= 2 x + y + 0

Simplify

= 2 x + y

x \to 2 lim (6 x^{2})

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

x \to - \infty lim (\frac{x}{- x})

12 x^{\frac{1}{2}}

x \to a lim (2 x - 1)

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