If x² y⁵=(x+y)⁷ , then d² y d x² is equal to

Step-by-step solution

Given, x² y⁵=(x+y)⁷ Taking log on both sides, we get 2 x+5 y=7 (x+y) On differentiating, we get aligned 2 x + 5 y d y d x &= 7 x+y (1+ d y d x ) & d y d x ( 7 x+y - 5 y )= 2 x - 7 x+y aligned d y d x = y x Again, differentiating, we get aligned d² y d x² &= x d y d x -y x² &= x (y / x)-y x² [ from Eq. (i)] &=0 aligned