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

The answer to (\partial)/(\partial x)(4x^2y-4x+3y^3) is 8xy-4

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

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

8 x y - 4

Solution steps

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

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

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

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

= 8 y x - 4 + 0

Simplify

= 8 x y - 4

\int_{1}^{e^{4}} x^{2} ln (x) d x

y e^{2 x} d x = (4 + e^{2 x}) d y

x y^{2} y^{^{'}} = y^{3} - x^{3}, y (1) = 2

n = 1 \sum \infty n (\frac{4}{5})^{n}

\int - 9 x e^{- 3 x} d x

What is (\partial)/(\partial x)(4x^2y-4x+3y^3) ?
The answer to (\partial)/(\partial x)(4x^2y-4x+3y^3) is 8xy-4