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

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

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

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

2 x y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y^{3} x - 0

Simplify

= 2 x y^{3}

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