Question

if log (x^3 - y^3/x^3 + y^3) = a, prove that dy/dx=y/x​

Answer 1

Answer:

Solution

log10(x3−y3x3+y3)=2

∴x3−y3x3+y3=102=100

∴x3−y3=100x3+100y3

∴101y3=−99x3∴y3=−99101x3

Differentiating both sides w.r.t. x, we get,

3y2dydx=−99101×3x2

∴dydx=−99x2101y2