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

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

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

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

8 x y - 2

Solution steps

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

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

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

\frac{\partial}{\partial x} (2 y^{3}) = 0

= 8 y x - 2 + 0

Simplify

= 8 x y - 2

\int_{0}^{\frac{π}{4}} 4 tan^{4} (x) d x

y = sin (sin (x)), (2 π, 0)

\int 7 x cos (2 x) d x

\int_{0}^{1} sin^{2} (2 π t) d t

\int_{0}^{2} \frac{1}{x ^{2} - 4 x + 3} d x

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