What is (\partial)/(\partial x)(2y^3-6y+x^2) ?

The answer to (\partial)/(\partial x)(2y^3-6y+x^2) is 2x

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(\partial)/(\partial x)(2y^3-6y+x^2)

\frac{\partial}{\partial x} (2 y^{3} - 6 y + x^{2})

2 x

Solution steps

\frac{\partial}{\partial x} (2 y^{3} - 6 y + x^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 y^{3}) - \frac{\partial}{\partial x} (6 y) + \frac{\partial}{\partial x} (x^{2})

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

\frac{\partial}{\partial x} (6 y) = 0

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

= 0 - 0 + 2 x

Simplify

= 2 x

\int_{0}^{\frac{π}{2}} x sin (x) d x

x \to 1 lim (+ f (x))

\int_{0}^{1} 4 - y - 2 y - 1 d y

\int (3 x^{2} + 2) (2 x^{3} + 4 x + 1)^{\frac{1}{2}} d x

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

What is (\partial)/(\partial x)(2y^3-6y+x^2) ?
The answer to (\partial)/(\partial x)(2y^3-6y+x^2) is 2x