equation of tangent at (e,e) on y = x lnx

y = x lnx

dy/dx = x(1/x) + lnx (1) = 1 + lnx

slope of tangent , m = (dy/dx) at (e,e) = 1 + ln(e) = 1 + 1 = 2

equation of tangent at (e,e) is
(y - y1) = m (x-x1)

y - e = 2(x-e)

or y = 2x - e
other examples
equation of tangent to y =x^4 at the point where x=2


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