What is the derivative of f(x)=3x^{-4} ?

The derivative of f(x)=3x^{-4} is -(12)/(x^5)

What is the first derivative of f(x)=3x^{-4} ?

The first derivative of f(x)=3x^{-4} is -(12)/(x^5)

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derivative of

f (x) = 3 x^{- 4}

- \frac{12}{x ^{5}}

Solution steps

\frac{d}{d x} (3 x^{- 4})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{- 4})

Apply the Power Rule:

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

= 3 (- 4 x^{- 4 - 1})

Simplify

3 (- 4 x^{- 4 - 1}) : - \frac{12}{x ^{5}}

= - \frac{12}{x ^{5}}

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What is the derivative of f(x)=3x^{-4} ?
The derivative of f(x)=3x^{-4} is -(12)/(x^5)
What is the first derivative of f(x)=3x^{-4} ?
The first derivative of f(x)=3x^{-4} is -(12)/(x^5)