What is the derivative of 5x^{-5}-6x^{-2}+13x^{-1} ?

The derivative of 5x^{-5}-6x^{-2}+13x^{-1} is -(25)/(x^6)+(12)/(x^3)-(13)/(x^2)

What is the first derivative of 5x^{-5}-6x^{-2}+13x^{-1} ?

The first derivative of 5x^{-5}-6x^{-2}+13x^{-1} is -(25)/(x^6)+(12)/(x^3)-(13)/(x^2)

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\frac{d}{d x} (5 x^{- 5} - 6 x^{- 2} + 13 x^{- 1})

- \frac{25}{x ^{6}} + \frac{12}{x ^{3}} - \frac{13}{x ^{2}}

Solution steps

\frac{d}{d x} (5 x^{- 5} - 6 x^{- 2} + 13 x^{- 1})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x^{- 5}) - \frac{d}{d x} (6 x^{- 2}) + \frac{d}{d x} (13 x^{- 1})

\frac{d}{d x} (5 x^{- 5}) = - \frac{25}{x ^{6}}

\frac{d}{d x} (6 x^{- 2}) = - \frac{12}{x ^{3}}

\frac{d}{d x} (13 x^{- 1}) = - \frac{13}{x ^{2}}

= - \frac{25}{x ^{6}} - (- \frac{12}{x ^{3}}) - \frac{13}{x ^{2}}

Simplify

= - \frac{25}{x ^{6}} + \frac{12}{x ^{3}} - \frac{13}{x ^{2}}

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\int_{0}^{6} e^{x} d x

(\frac{y}{x} + 9 x) d x + (ln (x) - 2) d y = 0

\int (x^{n} ln (x)) d x

\int_{- 2}^{0} 3 w 4 - w^{2} d w

What is the derivative of 5x^{-5}-6x^{-2}+13x^{-1} ?
The derivative of 5x^{-5}-6x^{-2}+13x^{-1} is -(25)/(x^6)+(12)/(x^3)-(13)/(x^2)
What is the first derivative of 5x^{-5}-6x^{-2}+13x^{-1} ?
The first derivative of 5x^{-5}-6x^{-2}+13x^{-1} is -(25)/(x^6)+(12)/(x^3)-(13)/(x^2)