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Question Number 165168 by saboorhalimi last updated on 26/Jan/22

Answered by mahdipoor last updated on 26/Jan/22

$$\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{3t^2}{3t^2-4}=1+\frac{4}{3t^2-4}$$$$\frac{d^{2}y}{{dx}^2}=\frac{d\left(dy/dx\right)}{dx}=\frac{\frac{d\left(dy/dx\right)}{dt}}{\frac{dx}{dt}}=\frac{\frac{-4\left(6t\right)}{{(3t^2-4)}^2}}{3t^2-4}=$$$$-\frac{24t}{{(3t^2-4)}^3}\stackrel{t=1}{\Rightarrow }=24$$

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