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Popular >

derivative of x^3+5x^2-x^{-2}+8

Solution

\frac{d}{d x} (x^{3} + 5 x^{2} - x^{- 2} + 8)

Solution

3 x^{2} + 10 x + \frac{2}{x ^{3}}

Solution steps

\frac{d}{d x} (x^{3} + 5 x^{2} - x^{- 2} + 8)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (5 x^{2}) - \frac{d}{d x} (x^{- 2}) + \frac{d}{d x} (8)

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

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

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

\frac{d}{d x} (8) = 0

= 3 x^{2} + 10 x - (- \frac{2}{x ^{3}}) + 0

Simplify

= 3 x^{2} + 10 x + \frac{2}{x ^{3}}

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Frequently Asked Questions (FAQ)

What is the derivative of x^3+5x^2-x^{-2}+8 ?
The derivative of x^3+5x^2-x^{-2}+8 is 3x^2+10x+2/(x^3)
What is the first derivative of x^3+5x^2-x^{-2}+8 ?
The first derivative of x^3+5x^2-x^{-2}+8 is 3x^2+10x+2/(x^3)