Question

Find the first derivative and second derivative of given functions with respect to corresponding independent variable : y= 6x² - 10x - 5x^-2​

Answer 1

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$y = 6 {x}^{2} - 10x - {5x}^{ - 2}$

$(first \: derivative \: )\frac{dy}{dx} = 12x - 10 + 2 \times 5 {x}^{ - 3}$

$\frac{dy}{dx} = 12x - 10 + 10 {x}^{ - 3}$

$(second \: derivative) \frac{ {d}^{2}y }{ {dx}^{2} } = 12 - 0 - 30 {x}^{ - 4}$

$\: \frac{ {d}^{2} y}{ {dx}^{2} } = 12 - 30 {x}^{ - 4}$