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

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

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(\partial)/(\partial x)(xy^3-x)

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

y^{3} - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y^{3} - 1

\int \frac{1}{324 - x ^{2}} d x

\int tan^{8} (7 x) sec^{4} (7 x) d x

f (x) = x^{2} - 1, at x = - 3

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

\frac{d}{d x} (5 - 8 x)

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