What is (\partial)/(\partial x)(4-2*(3x-y)^2) ?

The answer to (\partial)/(\partial x)(4-2*(3x-y)^2) is -12(3x-y)

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(\partial)/(\partial x)(4-2*(3x-y)^2)

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

- 12 (3 x - y)

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (4) = 0

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

= 0 - 12 (3 x - y)

Simplify

= - 12 (3 x - y)

y = - (- 6 x + 6)^{\frac{1}{2}}, x = - 5

\frac{d}{d v} (a e^{v} + \frac{b}{v} + \frac{c}{v ^{2}})

x y^{^{'}} - 2 y + y^{2} = 0

y^{^{''}} + 2 k y^{^{'}} + k^{4} y = 0

(9, 12), (- 2, - 17)

What is (\partial)/(\partial x)(4-2*(3x-y)^2) ?
The answer to (\partial)/(\partial x)(4-2*(3x-y)^2) is -12(3x-y)