निम्न फलनों के लिए ` (d^(2)y)/(dx^(2) )` का मान ज्ञात कीजिये|
`(i) x=at^(2), y= 2at `
`(ii) x=a cos theta , y= bsin theta `
`(iii) x=a cos ^(3) theta ,y= asin ^(3) theta `

Answer

` (i) -(1)/(2at^(3))(ii) -(b^(4) )/(a^(2)y^(3))(iii) (1)/(3a )sec ^(4) theta cosectheta `

Explanation

` (i) x= at^(2) " "rArr (dx)/(dt) =2at , y= 2at rArr(dy)/(dt)=2a`
`therefore " "(dy)/(dx) =(dy)/(dx) xx (dt)/(dx) =(2a)/(2at) =(1)/(t)`
अब ` (d^(2)y)/(dx^(2) )=(d)/(dx) ((dy)/(dx) ) =(d)/(dx)((1)/(t))=(d)/(dt ) ((1)/(t))*(dt)/(dx) `