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

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Answer 1 · 2018-06-26T10:00:48

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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 #

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