If u=x^2+y^2 and x=s+3 t, y=2 s-t , then d^2 u d s^2 is equal to

Step-by-step solution

Given that, u=x^2+y^2 and x=s+3 t, y=2 s-t Now, u=x^2+y^2 aligned & =(s+3 t)^2+(2 s-t)^2 & =s^2+9 t^2+6 s t+4 s^2+t^2-4 s t u & =5 s^2+2 s t+10 t^2 aligned On differentiating with respect to s , we get d u d s =10 s+2 t Again differentiating d^2 u d s^2 =10