What is the derivative of (x^{-12}(x^{-12})) ?

The derivative of (x^{-12}(x^{-12})) is -(24)/(x^{25)}

What is the first derivative of (x^{-12}(x^{-12})) ?

The first derivative of (x^{-12}(x^{-12})) is -(24)/(x^{25)}

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

- \frac{24}{x ^{25}}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 12}, g = x^{- 12}

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

\frac{d}{d x} (x^{- 12}) = - \frac{12}{x ^{13}}

\frac{d}{d x} (x^{- 12}) = - \frac{12}{x ^{13}}

= (- \frac{12}{x ^{13}}) x^{- 12} + (- \frac{12}{x ^{13}}) x^{- 12}

Simplify

(- \frac{12}{x ^{13}}) x^{- 12} + (- \frac{12}{x ^{13}}) x^{- 12} : - \frac{24}{x ^{25}}

= - \frac{24}{x ^{25}}

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What is the derivative of (x^{-12}(x^{-12})) ?
The derivative of (x^{-12}(x^{-12})) is -(24)/(x^{25)}
What is the first derivative of (x^{-12}(x^{-12})) ?
The first derivative of (x^{-12}(x^{-12})) is -(24)/(x^{25)}