Question

x^y-y^x = a^b find dy/dx

Answer 1

Step-by-step explanation:

x^y - y^x = a^b

Taking log

ylogx - xlogy = bloga

D.w.r.to.x

y×1/x + logx*dy/dx - (x/y*dy/dx + logy) = 0

y/x - logy + (logx - x/y)dy/dx = 0

(ylogx - x )/y*dy/dx = (xlogy-y )/x

dy/dx = y(xlogy-y)/x(ylogx-x)

dy/dx = xy(logy - y/x) / xy(logx - x/y)

= (logy - y/x ) / (logx - x/y )