Given that y=x^5 + 1/(x^2), find

(i) \frac{\text{d}y}{\text{d}x}

(ii) \frac{d^2y}{dx^2}

 

Answer (i)

y=x^5 + 1/(x^2)

or y=x^5 + x^{-2}

\therefore \frac{\text{d}y}{\text{d}x} = 5x^4-2x^{-3}

Answer (ii)

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

\therefore \frac{d^2y}{dx^2} = 5\times4x^3-2\times(-3)x^{-4}

or, \frac{d^2y}{dx^2} = 20x^3+6x^{-4}

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