if x*2y*3=(x+y)*5 find dy/dx
Answers
Answered by
1
Given that,
x² y³ = (x + y)⁵
Taking (log) in both sides, we get
log (x² y³) = log { (x + y)⁵ }
or, 2 logx + 3 logy = 5 log (x+ y)
Now, differentiating both sides with respect to x, we get
2/x + 3/y dy/dx = 5/(x + y) (1 + dy/dx)
or, {3/y - 5/(x + y)} dy/dx = 5/(x + y) - 2/x
or, (3x + 3y - 5y)/{y (x + y)} dy/dx
= (5x - 2x - 2y)/{ x (x + y)}
or, (3x - 2y)/y dy/dx = (3x - 2y)/x
or, dy/dx = y/x
Therefore,
#
rk9640pa1dbq:
i had solved this problem... but ur way is impressive..
Similar questions