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

The answer to (\partial)/(\partial x)(2x^2y-x+3y^3) is 4xy-1

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

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

4 x y - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

= 4 y x - 1 + 0

Simplify

= 4 x y - 1

\frac{d}{d x} ((x - 2) (- x + 2) (x^{2} + 3 x - 3))

y^{^{''}} - 8 y^{^{'}} + 15 y = 0

x \to \infty lim (csc (9))

y = (4 x - 1)^{2} (x^{4} + 1)^{2}

\frac{\partial}{\partial x} (\frac{x z + yz}{x y})

What is (\partial)/(\partial x)(2x^2y-x+3y^3) ?
The answer to (\partial)/(\partial x)(2x^2y-x+3y^3) is 4xy-1