differentiate 1/x — step-by-step solution

To ease differentiation, the expression

\frac{1}{x}

is turned into

x^{-1}

Let's differentiate:

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

We differentiate using:

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

(where f =

x

)

ⓘ The derivative of x^n is n*x^(n-1):

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

-1 \cdot x^{-2}

-1 \cdot x^{-2}

ⓘ Multiplying by -1 gives the opposite:

-1 \cdot x^{-2}

- x^{-2}

- x^{-2}

ⓘ The factor is moved to the numerator or the denominator by changing the sign of its exponent, for a nonzero base:

- x^{-2}

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

▶Derivative:

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