What is (\partial)/(\partial x)(3x^2-2x+6y^2+2y+2) ?

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

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(\partial)/(\partial x)(3x^2-2x+6y^2+2y+2)

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 y + 2)

6 x - 2

Solution steps

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 y + 2)

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} (2 x) + \frac{\partial}{\partial x} (6 y^{2}) + \frac{\partial}{\partial x} (2 y) + \frac{\partial}{\partial x} (2)

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

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

\frac{\partial}{\partial x} (6 y^{2}) = 0

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

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

= 6 x - 2 + 0 + 0 + 0

Simplify

= 6 x - 2

\int (u^{4} - u^{3} + u^{2}) d u

\frac{\partial}{\partial x} (4 y - 2 x y)

sin (2 x)

x \to 2 lim (\frac{1}{( x - 2 )})

\int \frac{2 x ^{3} + x ^{2} - 7 x + 7}{x ^{2} + x - 2} d x

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