What is the derivative of x^{-2}(4+3x^{-3}) ?

The derivative of x^{-2}(4+3x^{-3}) is (-8x^3-15)/(x^6)

What is the first derivative of x^{-2}(4+3x^{-3}) ?

The first derivative of x^{-2}(4+3x^{-3}) is (-8x^3-15)/(x^6)

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\frac{d}{d x} (x^{- 2} (4 + 3 x^{- 3}))

\frac{- 8 x ^{3} - 15}{x ^{6}}

Solution steps

\frac{d}{d x} (x^{- 2} (4 + 3 x^{- 3}))

Apply the Product Rule:

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

f = x^{- 2}, g = 4 + 3 x^{- 3}

= \frac{d}{d x} (x^{- 2}) (4 + 3 x^{- 3}) + \frac{d}{d x} (4 + 3 x^{- 3}) x^{- 2}

\frac{d}{d x} (x^{- 2}) = - \frac{2}{x ^{3}}

\frac{d}{d x} (4 + 3 x^{- 3}) = - \frac{9}{x ^{4}}

= (- \frac{2}{x ^{3}}) (4 + 3 x^{- 3}) + (- \frac{9}{x ^{4}}) x^{- 2}

Simplify

(- \frac{2}{x ^{3}}) (4 + 3 x^{- 3}) + (- \frac{9}{x ^{4}}) x^{- 2} : \frac{- 8 x ^{3} - 15}{x ^{6}}

= \frac{- 8 x ^{3} - 15}{x ^{6}}

What is the derivative of x^{-2}(4+3x^{-3}) ?
The derivative of x^{-2}(4+3x^{-3}) is (-8x^3-15)/(x^6)
What is the first derivative of x^{-2}(4+3x^{-3}) ?
The first derivative of x^{-2}(4+3x^{-3}) is (-8x^3-15)/(x^6)