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

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

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

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

2 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x - 0

Simplify

= 2 x y

y^{^{'}} = (2 y + 1) cot (x)

\frac{d}{d x} (\frac{3 x ^{2}}{x ^{2} + 1})

y = \frac{x - 2}{x + 2}

f (x) = 7 x e^{x}, at x = 0

\frac{d}{d x} (5 x^{\frac{3}{5}} - 4)

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