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

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

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

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

6 x^{2}

Solution steps

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

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} (y)

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

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

= 6 x^{2} + 0

Simplify

= 6 x^{2}

\int + \frac{4 - 32 x}{1 - 16 x ^{2}} d x

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

x^{2} \frac{d y}{d x} + x y = 1

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

\frac{\partial ^{3}}{\partial x \partial y \partial z} (e^{x y z^{6}})

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