What is the derivative of (1/x)(x^2-2) ?

The derivative of (1/x)(x^2-2) is -(x^2-2)/(x^2)+2

What is the first derivative of (1/x)(x^2-2) ?

The first derivative of (1/x)(x^2-2) is -(x^2-2)/(x^2)+2

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derivative

- \frac{x ^{2} - 2}{x ^{2}} + 2

Solution steps

\frac{d}{d x} (\frac{1}{x} (x^{2} - 2))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x}, g = x^{2} - 2

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

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

\frac{d}{d x} (x^{2} - 2) = 2 x

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

Simplify

(- \frac{1}{x ^{2}}) (x^{2} - 2) + 2 x \frac{1}{x} : - \frac{x ^{2} - 2}{x ^{2}} + 2

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

What is the derivative of (1/x)(x^2-2) ?
The derivative of (1/x)(x^2-2) is -(x^2-2)/(x^2)+2
What is the first derivative of (1/x)(x^2-2) ?
The first derivative of (1/x)(x^2-2) is -(x^2-2)/(x^2)+2