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

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

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

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

6 x^{2} - 6 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial x} (2) = 0

= 6 x^{2} + 0 - 6 y + 0

Simplify

= 6 x^{2} - 6 y

\frac{d}{d x} ((2 x^{4} - x + 1) (- x^{5} + 4))

\int 5 x^{9} d x

4 t^{\frac{1}{2}}

4 - x^{2}, 2 - x

\frac{d}{d x} (16 x e^{- x})

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