Question

14.If x1/2 + y 1/2 = a 1/2, find the value of d²y/dx2 at x= a
​

Answer 1

Given,

x=at

2

and y=2at

On differentiating both sides w.r.t. t, we get,

dt

dx

=2at and

dt

dy

=2a

Therefore,

dx

dy

=

2at

2a

=

t

1

Now,

dx

2

d

2

y

=

dt

d

(

dx

dy

)×

dx

dt

=

dt

d

(

t

1

)×

2at

1

=−

t

2

1

×

2at

1

=−

2at

3

1

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