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CBSE Class 12-science Answered

Q - (ix), find the second order derivative.
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Asked by majethiyarishat9566.12sdatl | 05 Jun, 2020, 07:09: PM
answered-by-expert Expert Answer
Given: 3x = t3 and 2y = t2
The above two equations are in parametric form which can be solved as follows:
 
Given: 3x=t3 and 2y=t2
 
Differentiating above equations w.r.t t, we get
 
3 dx/dt = 3t2  and  2 dy/dt = 2t
 
dx/dt = t2  ... (i)  and  dy/dt = t  ... (ii)
 
Dividing (ii) by (i), we get
 
(dy/dt)/(dx/dt) = t/t2
 
Therefore, dy/dx = 1/t
Differentiating w.r.t x, we get
d2y/dx2 = -1/t2 dt/dx
= -1/t2 (1/t2)   ... From (i)
= -1/t4
Hence, d2y/dx2 = -1/t4
Answered by Renu Varma | 08 Jun, 2020, 10:41: AM
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