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

The answer to (\partial}{\partial x}(\frac{x^2-1)/y) is (2x)/y

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

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

\frac{2 x}{y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{y} (2 x - 0)

Simplify

\frac{1}{y} (2 x - 0) : \frac{2 x}{y}

= \frac{2 x}{y}

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