Question

X16 y9 = (x2 + y)17 prove that x dy/dx = 2y - math sum

Answer 1

x16.y9=(x2+y)17

Taking log both sides,

16logx+9logy=17log(x2+y)

Differentiating both sides with respect to 'x'

16/x+9/y.dy/dx= 17/x2+y*(2x+dy/dx)

=> 9/y-17/x2+y=34x/x2+y-16/x

=> 9x2+9y-17y/ (x2+y)y[dy/dx] = 34x2-16x2-16y/x(x2+y)

=> 9x2-8y/y(x2+y) [dy/dx]= 18x2-16y/x(x2+y)

=> 9x2-8y/y [dy/dx]= 2[9x2-8y]/x

=> 1/y dy/dx =2/x

=> xdy/dx=2y

Hence Proved.