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

The derivative of x(-3x^{-4}) is 9/(x^4)

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

The first derivative of x(-3x^{-4}) is 9/(x^4)

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derivative of

x (- 3 x^{- 4})

\frac{9}{x ^{4}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = - 3 x^{- 4}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (- 3 x^{- 4}) = \frac{12}{x ^{5}}

= 1 \cdot (- 3 x^{- 4}) + \frac{12}{x ^{5}} x

Simplify

1 \cdot (- 3 x^{- 4}) + \frac{12}{x ^{5}} x : \frac{9}{x ^{4}}

= \frac{9}{x ^{4}}

What is the derivative of x(-3x^{-4}) ?
The derivative of x(-3x^{-4}) is 9/(x^4)
What is the first derivative of x(-3x^{-4}) ?
The first derivative of x(-3x^{-4}) is 9/(x^4)