Math, asked by rk9640pa1dbq, 1 year ago

if x*2y*3=(x+y)*5 find dy/dx

Answers

Answered by MarkAsBrainliest
1
\bold{Answer :}

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, \bold{dy/dx = y/x}

#\textbf{MarkAsBrainliest}

rk9640pa1dbq: i had solved this problem... but ur way is impressive..
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