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

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

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(\partial)/(\partial x)(x^2-xy^3+1)

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

2 x - y^{3}

Solution steps

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

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

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

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

= 2 x - y^{3} + 0

Simplify

= 2 x - y^{3}

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