Question

find dy/dx if y= at² and x = at​

Answer 1

Step-by-step explanation:

dy/dt= 2at

dx/dt=a

dy/dx= (dy/dt) / (dx/dt)

=2at/a

=2t

so, dy/dx if y= at² and x = at is 2t

Answer 2

Given : y = at²  ,   x =  at

To Find : dy/dx

Solution:

y = at²

dy/dt  = 2at

x =  at

dx/dt  = a

(dy/dx)  = (dy/dt )/  (dx/dt)  =  2at/a

=> dy/dx  = 2t

Another method:

y = at²

=> dy/dx  = 2at. dt/dx

x =  at

=> t = x/a

=> dt/dx  = 1/a

Substitute  dt/dx= 1/a  in   dy/dx  = 2at. dt/dx

=> dy/dx  = 2at. (1/a)

=>  dy/dx  = 2t  

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