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

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

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

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

6 x^{2} y

Solution steps

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

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

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

= 6 y x^{2} + 0

Simplify

= 6 x^{2} y

\frac{1}{( 1 + 4 x )}

\frac{\partial}{\partial x} (cos (y^{2}) + y e^{x})

\int \frac{1}{x ^{2} + 6 x + 6} d x

\frac{d y}{d x} + 2 x y = x^{3}

\frac{\partial}{\partial y} (\frac{- y}{x ^{2} + 9 y ^{2}})

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