What is the derivative of 5x^{-1} ?

The derivative of 5x^{-1} is -5/(x^2)

What is the first derivative of 5x^{-1} ?

The first derivative of 5x^{-1} is -5/(x^2)

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derivative of

5 x^{- 1}

- \frac{5}{x ^{2}}

Solution steps

\frac{d}{d x} (5 x^{- 1})

Take the constant out:

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

= 5 \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

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

= 5 (- 1 \cdot x^{- 1 - 1})

Simplify

5 (- 1 \cdot x^{- 1 - 1}) : - \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

\frac{\partial}{\partial x} (A^{3} (\frac{x}{d})^{2})

\frac{d}{d x} (\frac{x ^{3}}{y})

\frac{d}{d y} (ln (x^{2} + y^{2}))

\frac{d}{d x} (\frac{6}{5} e^{- 20 x})

ln (\frac{x}{2}), x = 2

What is the derivative of 5x^{-1} ?
The derivative of 5x^{-1} is -5/(x^2)
What is the first derivative of 5x^{-1} ?
The first derivative of 5x^{-1} is -5/(x^2)