Question

If u = x² + y² and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = ______ 

Options

• 12

• 32

• 36

• 10

Answer 1

If u = x² + y² and x = s + 3t, y = 2s - t, then `(d^2u)/(ds^2)` = 10

Explanation:

Here, `dx/(ds) = 1`, `dy/(ds) = 2` .............(i)

and `(d^2x)/(ds^2) = 0, (d^2y)/(ds^2) = 0` .............(ii)

Now, u = x² + y²

∴ `(du)/(ds) = 2x . dx/(ds) + 2y. dy/(ds)`

∴ `(d^2u)/(ds^2) = 2(dx/(ds))^2 + 2x((d^2x)/(ds^2)) + 2(dy/(ds))^2 + 2y((d^2y)/(ds^2))`

From (i) and (ii), we get

`(d^2u)/(ds^2) = 2(1) + 0 + 2(4) + 0 = 10`