(1/X)^'

Solution

(\frac{1}{X})^{^{'}}

- \frac{1}{X ^{2}}

Solution steps

(\frac{1}{X})^{'}

Apply exponent rule:

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

= (X^{- 1})^{^{'}}

Apply the Power Rule:

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

= - 1 \cdot X^{- 1 - 1}

Simplify

- 1 \cdot X^{- 1 - 1} : - \frac{1}{X ^{2}}

= - \frac{1}{X ^{2}}

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

\frac{d}{d x} (\frac{( 2 x - 3 ) ^{- 3}}{( 2 - 3 x ) ^{2}})

x \to 0 lim (\frac{x ^{4} + 1}{x ^{2}})

x \to 0 lim (∣ sin (x) ∣^{x})

\int \frac{6 x ^{2} - 2 x - 1}{4 x ^{3} - x} d x