What is the derivative of pix^7-2x^5-5x^{-2} ?

The derivative of pix^7-2x^5-5x^{-2} is 7pix^6-10x^4+(10)/(x^3)

What is the first derivative of pix^7-2x^5-5x^{-2} ?

The first derivative of pix^7-2x^5-5x^{-2} is 7pix^6-10x^4+(10)/(x^3)

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\frac{d}{d x} (π x^{7} - 2 x^{5} - 5 x^{- 2})

7 π x^{6} - 10 x^{4} + \frac{10}{x ^{3}}

Solution steps

\frac{d}{d x} (π x^{7} - 2 x^{5} - 5 x^{- 2})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (π x^{7}) - \frac{d}{d x} (2 x^{5}) - \frac{d}{d x} (5 x^{- 2})

\frac{d}{d x} (π x^{7}) = 7 π x^{6}

\frac{d}{d x} (2 x^{5}) = 10 x^{4}

\frac{d}{d x} (5 x^{- 2}) = - \frac{10}{x ^{3}}

= 7 π x^{6} - 10 x^{4} - (- \frac{10}{x ^{3}})

Simplify

= 7 π x^{6} - 10 x^{4} + \frac{10}{x ^{3}}

What is the derivative of pix^7-2x^5-5x^{-2} ?
The derivative of pix^7-2x^5-5x^{-2} is 7pix^6-10x^4+(10)/(x^3)
What is the first derivative of pix^7-2x^5-5x^{-2} ?
The first derivative of pix^7-2x^5-5x^{-2} is 7pix^6-10x^4+(10)/(x^3)