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

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

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

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

2 x + 3 y

Solution steps

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

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

\frac{\partial}{\partial x} (3 x y) = 3 y

= 2 x + 3 y

y = \frac{x}{6} - \frac{6}{x}

\frac{\partial}{\partial x} (- 0.1 \cdot cos (6 \cdot x))

x \to 0 lim (\frac{- 11 x ^{2} + 9 x}{x})

\int x sin (3 + 3 x) d x

\int (\frac{1}{5} x^{5} + \frac{1}{3} x^{4} - x) d x

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