What is the derivative of-2/x ?

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

What is the first derivative of-2/x ?

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

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derivative of

- \frac{2}{x}

\frac{2}{x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the Power Rule:

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

= - 2 (- 1 \cdot x^{- 1 - 1})

Simplify

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

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

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

3 x^{2} + 8 x + 2

x \to 0 lim (\frac{2 ( x + h ( x ) ) - 2 x}{h ( x )})

y^{^{''}} + y = 0, y (0) = 1, y^{^{'}} (0) = 1

5 t^{3}