What is (\partial)/(\partial x)(3x^2+12x+2xy+8y) ?

The answer to (\partial)/(\partial x)(3x^2+12x+2xy+8y) is 6x+2y+12

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(\partial)/(\partial x)(3x^2+12x+2xy+8y)

\frac{\partial}{\partial x} (3 x^{2} + 12 x + 2 x y + 8 y)

6 x + 2 y + 12

Solution steps

\frac{\partial}{\partial x} (3 x^{2} + 12 x + 2 x y + 8 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (12 x) + \frac{\partial}{\partial x} (2 x y) + \frac{\partial}{\partial x} (8 y)

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

\frac{\partial}{\partial x} (12 x) = 12

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

\frac{\partial}{\partial x} (8 y) = 0

= 6 x + 12 + 2 y + 0

Simplify

= 6 x + 2 y + 12

\frac{d}{d x} (\frac{4 x - 7}{x - 2})

\int e^{4 x - 2} d x

x + \frac{6}{x}

\int - cos (x) d x

x^{4} sin (x) tan (x)

What is (\partial)/(\partial x)(3x^2+12x+2xy+8y) ?
The answer to (\partial)/(\partial x)(3x^2+12x+2xy+8y) is 6x+2y+12