Question

find d^2y/dx^2 i) x=ct. , y =c/t​

Answer 1

Step-by-step explanation:

$x = ct = > \frac{dx}{dt} = c \: .....(i)$

$y = \frac{c}{t} = > \frac{dy}{dt} = - \frac{c}{ {t}^{2} } \: ....(ii)$

From (i) and (ii),

$\frac{dy}{dx} = \frac{ \frac{ - c}{ {t}^{2} } }{c}$

$= > \frac{ {d}^{2}y }{d {x}^{2} } = - \frac{d}{dt} ( \frac{1}{ {t}^{2} } ). \frac{dt}{dx}$

$= > \frac{ {d}^{2}y }{d {x}^{2} } = - ( \frac{1}{ {t}^{2} } ) \frac{1}{c}$