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

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

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

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

6 y - 12

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (3 x^{2}) = 0

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

= 6 y + 0 - 12

Simplify

= 6 y - 12

y^{^{'}} = 3 e^{- 2 x}

f (x) = \frac{1}{x}, (1, 3)

\frac{\partial}{\partial x} (sin (- 3 x + 1 y + z))

\int (\frac{2 x ^{5} - 4 x + 8 x}{x}) d x

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

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