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

The derivative of (x^3-2x)(x^{-4}+x^{-2}) is 1/(x^2)+6/(x^4)+1

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

The first derivative of (x^3-2x)(x^{-4}+x^{-2}) is 1/(x^2)+6/(x^4)+1

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derivative of

(x^{3} - 2 x) (x^{- 4} + x^{- 2})

\frac{1}{x ^{2}} + \frac{6}{x ^{4}} + 1

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (x^{- 4} + x^{- 2}) = - \frac{4}{x ^{5}} - \frac{2}{x ^{3}}

= (3 x^{2} - 2) (x^{- 4} + x^{- 2}) + (- \frac{4}{x ^{5}} - \frac{2}{x ^{3}}) (x^{3} - 2 x)

Simplify

(3 x^{2} - 2) (x^{- 4} + x^{- 2}) + (- \frac{4}{x ^{5}} - \frac{2}{x ^{3}}) (x^{3} - 2 x) : \frac{1}{x ^{2}} + \frac{6}{x ^{4}} + 1

= \frac{1}{x ^{2}} + \frac{6}{x ^{4}} + 1

What is the derivative of (x^3-2x)(x^{-4}+x^{-2}) ?
The derivative of (x^3-2x)(x^{-4}+x^{-2}) is 1/(x^2)+6/(x^4)+1
What is the first derivative of (x^3-2x)(x^{-4}+x^{-2}) ?
The first derivative of (x^3-2x)(x^{-4}+x^{-2}) is 1/(x^2)+6/(x^4)+1