What is (\partial)/(\partial y)(3x^2+2y^2-4xy+5) ?

The answer to (\partial)/(\partial y)(3x^2+2y^2-4xy+5) is 4y-4x

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(\partial)/(\partial y)(3x^2+2y^2-4xy+5)

\frac{\partial}{\partial y} (3 x^{2} + 2 y^{2} - 4 x y + 5)

4 y - 4 x

Solution steps

\frac{\partial}{\partial y} (3 x^{2} + 2 y^{2} - 4 x y + 5)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (3 x^{2}) + \frac{\partial}{\partial y} (2 y^{2}) - \frac{\partial}{\partial y} (4 x y) + \frac{\partial}{\partial y} (5)

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

\frac{\partial}{\partial y} (2 y^{2}) = 4 y

\frac{\partial}{\partial y} (4 x y) = 4 x

\frac{\partial}{\partial y} (5) = 0

= 0 + 4 y - 4 x + 0

Simplify

= 4 y - 4 x

\int_{- 1}^{2} (2 + x - x^{2}) d x

x \to \frac{1}{3} lim (\frac{x + 1}{x + 2})

x \to 3 lim (1)

\frac{d}{d x} (8 x^{2} + 1)

\frac{d}{d x} ((sin (2 x)) (cos (2 x)))

What is (\partial)/(\partial y)(3x^2+2y^2-4xy+5) ?
The answer to (\partial)/(\partial y)(3x^2+2y^2-4xy+5) is 4y-4x