What is (\partial)/(\partial x)(12x^2-9xy+16y^2) ?

The answer to (\partial)/(\partial x)(12x^2-9xy+16y^2) is 24x-9y

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(\partial)/(\partial x)(12x^2-9xy+16y^2)

\frac{\partial}{\partial x} (12 x^{2} - 9 x y + 16 y^{2})

24 x - 9 y

Solution steps

\frac{\partial}{\partial x} (12 x^{2} - 9 x y + 16 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (12 x^{2}) - \frac{\partial}{\partial x} (9 x y) + \frac{\partial}{\partial x} (16 y^{2})

\frac{\partial}{\partial x} (12 x^{2}) = 24 x

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

\frac{\partial}{\partial x} (16 y^{2}) = 0

= 24 x - 9 y + 0

Simplify

= 24 x - 9 y

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What is (\partial)/(\partial x)(12x^2-9xy+16y^2) ?
The answer to (\partial)/(\partial x)(12x^2-9xy+16y^2) is 24x-9y