Answer:
[tex] \purple{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
Step-by-step explanation:
[tex]y = \frac{1}{ {x}^{11} } \\ y = {x}^{ - 11} \\ \frac{dy}{dx} = \frac{d}{dx} {x}^{ - 11} \\ \frac{dy}{dx} = - 11{x}^{ - 11 - 1} \\ \frac{dy}{dx} = - 11{x}^{ - 12} \\ \\ \frac{d}{dx} \bigg(\frac{dy}{dx} \bigg) = \frac{d}{dx} ( - 11 {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11\frac{d}{dx} ( {x}^{ - 12} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = - 11( - 12{x}^{ - 13} ) \\ \\ \frac{d^{2} y}{dx ^{2} } = 132{x}^{ - 13} \\ \\ \huge \red{ \boxed{\frac{d^{2} y}{dx ^{2} } = \frac{132}{ {x}^{13} } }}[/tex]
