What is the derivative of x^4+5x^{-1} ?

The derivative of x^4+5x^{-1} is 4x^3-5/(x^2)

What is the first derivative of x^4+5x^{-1} ?

The first derivative of x^4+5x^{-1} is 4x^3-5/(x^2)

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\frac{d}{d x} (x^{4} + 5 x^{- 1})

4 x^{3} - \frac{5}{x ^{2}}

Solution steps

\frac{d}{d x} (x^{4} + 5 x^{- 1})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{4}) + \frac{d}{d x} (5 x^{- 1})

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

\frac{d}{d x} (5 x^{- 1}) = - \frac{5}{x ^{2}}

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

What is the derivative of x^4+5x^{-1} ?
The derivative of x^4+5x^{-1} is 4x^3-5/(x^2)
What is the first derivative of x^4+5x^{-1} ?
The first derivative of x^4+5x^{-1} is 4x^3-5/(x^2)