What is the derivative of y=3x^{-2}-5x^{-3}+3x^{-1} ?

The derivative of y=3x^{-2}-5x^{-3}+3x^{-1} is -6/(x^3)+(15)/(x^4)-3/(x^2)

What is the first derivative of y=3x^{-2}-5x^{-3}+3x^{-1} ?

The first derivative of y=3x^{-2}-5x^{-3}+3x^{-1} is -6/(x^3)+(15)/(x^4)-3/(x^2)

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derivative of

y = 3 x^{- 2} - 5 x^{- 3} + 3 x^{- 1}

- \frac{6}{x ^{3}} + \frac{15}{x ^{4}} - \frac{3}{x ^{2}}

Solution steps

\frac{d}{d x} (3 x^{- 2} - 5 x^{- 3} + 3 x^{- 1})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{- 2}) - \frac{d}{d x} (5 x^{- 3}) + \frac{d}{d x} (3 x^{- 1})

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

\frac{d}{d x} (5 x^{- 3}) = - \frac{15}{x ^{4}}

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

= - \frac{6}{x ^{3}} - (- \frac{15}{x ^{4}}) - \frac{3}{x ^{2}}

Simplify

= - \frac{6}{x ^{3}} + \frac{15}{x ^{4}} - \frac{3}{x ^{2}}

What is the derivative of y=3x^{-2}-5x^{-3}+3x^{-1} ?
The derivative of y=3x^{-2}-5x^{-3}+3x^{-1} is -6/(x^3)+(15)/(x^4)-3/(x^2)
What is the first derivative of y=3x^{-2}-5x^{-3}+3x^{-1} ?
The first derivative of y=3x^{-2}-5x^{-3}+3x^{-1} is -6/(x^3)+(15)/(x^4)-3/(x^2)