What is (\partial)/(\partial x)(4x^2+xy+3y^2-8) ?

The answer to (\partial)/(\partial x)(4x^2+xy+3y^2-8) is 8x+y

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(\partial)/(\partial x)(4x^2+xy+3y^2-8)

\frac{\partial}{\partial x} (4 x^{2} + x y + 3 y^{2} - 8)

8 x + y

Solution steps

\frac{\partial}{\partial x} (4 x^{2} + x y + 3 y^{2} - 8)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (3 y^{2}) - \frac{\partial}{\partial x} (8)

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

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

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

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

= 8 x + y + 0 - 0

Simplify

= 8 x + y

What is (\partial)/(\partial x)(4x^2+xy+3y^2-8) ?
The answer to (\partial)/(\partial x)(4x^2+xy+3y^2-8) is 8x+y