if x= a(t+sint) ;y=a(1-cost) then y2 that is second order derivative can we take second order derivative first and then divide??

Dear student
 
you can only find first order derivative that way.
 

Here x =a(t+Sint) and y =a(1-cost)

Differentiating both sides w r t.t,

We get

dx/dt =a(1+cost) and dt/dt =a(Sint)

Since dy/dx =(a sint)/a(1+cost)

dy/dx =2 sin(t/2) cos(t/2) /2cos^2 (t/2)

dy/dx =tan(t/2)

Again differentiating both sides we get

d^2 y /dx^2 =sec^2 (t/2) × 1/2 × dt/dx

d^2 y /d^2 x =1/2 [sec^2 (t/2) ×1/a(1+cost) ]

d^2 y /dx^2 =1/2[sec^2 (t/2) /2a cos^2 (t/2) ]

Hence d^2 y /dx^2 =1/4a sec^4 (t/2)