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

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

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

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

12 x^{2} + 2 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 12 x^{2} + 2 y x - 0

Simplify

= 12 x^{2} + 2 x y

\int_{1}^{e} ln (17 x) d x

\frac{d y}{d t} = 5

\frac{d}{d x} (arccos (e^{4 x}))

n = 1 \sum \infty sin (n)

y^{^{'}} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 4

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