What is the derivative of (12/x) ?

The derivative of (12/x) is -(12)/(x^2)

What is the first derivative of (12/x) ?

The first derivative of (12/x) is -(12)/(x^2)

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\frac{d}{d x} (\frac{12}{x})

- \frac{12}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{12}{x})

Take the constant out:

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

= 12 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 12 \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

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

= 12 (- 1 \cdot x^{- 1 - 1})

Simplify

12 (- 1 \cdot x^{- 1 - 1}) : - \frac{12}{x ^{2}}

= - \frac{12}{x ^{2}}

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\frac{d}{d x} (m x^{m + 5} + 6 x^{m} y^{n} + n x^{n + 3})

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What is the derivative of (12/x) ?
The derivative of (12/x) is -(12)/(x^2)
What is the first derivative of (12/x) ?
The first derivative of (12/x) is -(12)/(x^2)