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

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

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

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

3 y x^{2} - 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 y x^{2} - 1

\int \frac{x ^{2} + 1}{x ^{3} + 3 x} d x

\int e^{x} \cdot (- 3) e^{e^{x} + 2} d x

\frac{d}{d x} (x 5^{2 x})

\int_{0}^{3} 1

\int \frac{9 + x ^{2}}{x ^{4}} d x

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