Question

Find d^2y/dx^2

If x = at^2 , y=2at

#Dont spam

Answer 1

$= = = = = = >$

Given functions

x= at^2 and y=2at

x= at^2

Diff wrt to t

dx/dt=a d/dt(t^2)= a(2t)

dx/dt=2at

Now, the function

y=2at

diff wrt t

dy/dt=2a d/dt (t)

= 2a

therefor

$\frac{dy}{dx} = \frac{ \frac{dy}{dt} }{ \frac{dx}{dt} }$

$= \frac{2a}{2at} = \frac{1}{t}$

Again diff wrt x , we get

d^2y/dx^2=-1/t^2 x dt/dx

=(-1/t^2)x(1/2at)

= -1/ 2at^3

[dy/dx=-1/2at^3]