What is (\partial)/(\partial x)(4yx^3-12y^2x^2) ?

The answer to (\partial)/(\partial x)(4yx^3-12y^2x^2) is 12yx^2-24y^2x

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(\partial)/(\partial x)(4yx^3-12y^2x^2)

\frac{\partial}{\partial x} (4 y x^{3} - 12 y^{2} x^{2})

12 y x^{2} - 24 y^{2} x

Solution steps

\frac{\partial}{\partial x} (4 y x^{3} - 12 y^{2} x^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 y x^{3}) - \frac{\partial}{\partial x} (12 y^{2} x^{2})

\frac{\partial}{\partial x} (4 y x^{3}) = 12 y x^{2}

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

= 12 y x^{2} - 24 y^{2} x

s e^{- s}

x \to 0 + lim (x^{\frac{3}{x}})

\frac{d}{d x} (cos (6 x^{3} - 4))

e^{- 2 ((t - 1))} \cdot 1 ((t - 1))

\int_{0}^{7} e^{x} sin (x) d x

What is (\partial)/(\partial x)(4yx^3-12y^2x^2) ?
The answer to (\partial)/(\partial x)(4yx^3-12y^2x^2) is 12yx^2-24y^2x