Find the equation of the tangent to the curve Find the equation of the tangent to the curve:
$$y = e^x +1$$
At the point:
$$(1, e+1)$$
My process:
$$Gradient: y' = e^x$$
Tangent: $$y-(e+1) = e^x(x-1)$$
$$y= xe^x-e^x+e+1$$
I don't understand where my mistake is. I found the derivative (gradient) and then put it into the gradient formula to find the equation of the tangent but I am still wrong and I don't know where?

At $(1, e+1)$, 
$$y' = e^{1} = e$$
Then,
$$y - (e + 1) = e(x - 1)$$
$$y = ex + 1$$
I think it is a careless mistake.
