Question

If x/(x-y) = log(a/(x-y) ) prove that dy/dx= 2 - x/y

Answer 1

$\frac{x}{x-y}=Log(\frac{a}{x-y})\\\\Differentiate:\\\\x=(x-y)\ Log(\frac{a}{x-y})\\\\1=(1-y')\ Log(\frac{a}{x-y})+(x-y)\ [\frac{x-y}{a}][-a\frac{(1-y')}{(x-y)^2}]\\\\1=\frac{(1-y')x}{x-y}-(1-y')\\\\2(x-y)=x-yy'\\\\y'=2-\frac{x}{y}$

Answer 2

Answer:

see the attachment

hope you understand