e^{ln(x)}=x

y = ln (x)

e^{ln(x)}=x

e^{y} = e^{ln(x)}=x,y=ln (x)

e^{y} =x,y= ln (x)

(d(e^{y}))/dx= (d(x))/dx

e^{y} dy/dx=1

(d(y))/dx= 1/e^{y} ,y= ln (x) **divide e**^{y} on both sides

(d(y))/dx= 1/e^{y} = 1/e^{ln(x)} , e^{ln(x)} = x

(d(y))/dx= (d(ln(x))/dx= 1/x