How do you find the equation of the tangent line #y=x-lnx# at #(e, e-1)#?

Question

↳Redirected from "Can mixtures be separated by chromatography?"

4816 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-26T10:00:48

Shown below

Find gradient by taking the derivative

#(dy)/(dx) = 1 - 1/x #

at #x = e => (dy)/(dx) = 1-1/e #

Use #y-y_0 = m(x-x_0 )#

#=> y +1 -e = (1-1/e) ( x -e) #

#=> y = (1-1/e)x #

Shown below
Desmos