What is (\partial)/(\partial x)(9-x^2+xy-3y^2) ?

The answer to (\partial)/(\partial x)(9-x^2+xy-3y^2) is y-2x

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(\partial)/(\partial x)(9-x^2+xy-3y^2)

\frac{\partial}{\partial x} (9 - x^{2} + x y - 3 y^{2})

y - 2 x

Solution steps

\frac{\partial}{\partial x} (9 - x^{2} + x y - 3 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (9) - \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (x y) - \frac{\partial}{\partial x} (3 y^{2})

\frac{\partial}{\partial x} (9) = 0

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

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

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

= 0 - 2 x + y - 0

Simplify

= y - 2 x

12 - x^{2}, x^{2} - 6, [- 3, 3]

y = \frac{1}{x}, (2, \frac{1}{2})

\frac{\partial}{\partial x} (e^{s i n (x)})

\frac{d}{d x} (16 - x)

x \to 0 lim (\frac{cos ( x - 1 )}{x})

What is (\partial)/(\partial x)(9-x^2+xy-3y^2) ?
The answer to (\partial)/(\partial x)(9-x^2+xy-3y^2) is y-2x