What is the derivative of x^2+2x-x^{-1}+x^{-3} ?

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

What is the first derivative of x^2+2x-x^{-1}+x^{-3} ?

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

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\frac{d}{d x} (x^{2} + 2 x - x^{- 1} + x^{- 3})

2 x + 2 + \frac{1}{x ^{2}} - \frac{3}{x ^{4}}

Solution steps

\frac{d}{d x} (x^{2} + 2 x - x^{- 1} + x^{- 3})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (2 x) - \frac{d}{d x} (x^{- 1}) + \frac{d}{d x} (x^{- 3})

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

\frac{d}{d x} (2 x) = 2

\frac{d}{d x} (x^{- 1}) = - \frac{1}{x ^{2}}

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

= 2 x + 2 - (- \frac{1}{x ^{2}}) - \frac{3}{x ^{4}}

Simplify

= 2 x + 2 + \frac{1}{x ^{2}} - \frac{3}{x ^{4}}

h^{^{'}} = 2 t^{2} - 3 e^{t}

f (x) = \frac{2}{x}, at x = 3

t^{- 1}

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

x \to 0 lim (\frac{e ^{- 4 x} - 1}{x})

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