What is the derivative of 1/x ?

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

What is the first derivative of 1/x ?

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

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derivative of

\frac{1}{x}

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

Solution steps

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

Apply exponent rule:

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

= \frac{d}{d x} (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}}

\frac{d}{d x} (ln (cosh (5 x)))

\frac{d}{d x} (\frac{4 + x}{x e ^{x}})

\int \frac{1}{3} e^{t} d t

f (x) = ln (\frac{5 x + 3}{5 x - 3})

x^{2} + x \frac{d y}{d x} = y