What is (\partial)/(\partial x)(2x^3y-1) ?

The answer to (\partial)/(\partial x)(2x^3y-1) is 6x^2y

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(\partial)/(\partial x)(2x^3y-1)

\frac{\partial}{\partial x} (2 x^{3} y - 1)

6 x^{2} y

Solution steps

\frac{\partial}{\partial x} (2 x^{3} y - 1)

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} (1)

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

\frac{\partial}{\partial x} (1) = 0

= 6 y x^{2} - 0

Simplify

= 6 x^{2} y

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

\frac{1}{8} \frac{d ^{2} x}{d t ^{2}} = - 2 x - 1 \frac{d x}{d t}

\int (2 x - 4) (x + 2) d x

x - 4, x = 8

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

What is (\partial)/(\partial x)(2x^3y-1) ?
The answer to (\partial)/(\partial x)(2x^3y-1) is 6x^2y