Question

find the third drevative of y=(x³-2x)²​

Answer 1

Step-by-step explanation:

We have,

$y = {( {x}^{3} - 2x) }^{2}$

$= > y = {x}^{6} + 4 {x}^{2} - 4 {x}^{4}$

$= > y = {x}^{6} - 4 {x}^{4} + 4 {x}^{2}$

$= > \frac{dy}{dx} = 6 {x}^{5} - 16 {x}^{3} + 8x$

$= > \frac{ {d}^{2}y }{d {x}^{2} } = 30 {x}^{4} - 48 {x}^{2} + 8$

$= > \frac{ {d}^{3}y }{d {x}^{3} } = 120 {x}^{3} - 96x + 0$