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

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

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

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

2 x + 3 y

Solution steps

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

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

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

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

= 2 x + 0 + 3 y

Simplify

= 2 x + 3 y

x \to 0 lim (\frac{1}{1 + x})

\frac{d}{d x} (6 x e^{- k x})

- 5 e^{- x} + 30 e^{- 5 x}

\int \frac{1 - 3 t}{t ^{2}} d t

f (x) = \frac{4 x ^{2} - 7 x + 5}{2 x + 3}

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