How do you differentiate $y=e^(x+1)+1$ ?

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Answer 1 · 2017-07-10T17:15:08

Given: $y=e^(x+1)+1$

Differentiate each term:

$dy/dx = (d(e^(x+1)))/dx + (d(1))/dx$

The derivative of a constant is 0:

$dy/dx = (d(e^(x+1)))/dx + 0$

$dy/dx = (d(e^(x+1)))/dx$

We digress to use the chain rule:

Let $u = x+1$ , then $(du)/dx = 1$

$(d(e^(x+1)))/dx = (d(e^u))/dx(du)/dx$

$(d(e^(x+1)))/dx = (e^u)(1)$

Reverse the substitution:

$(d(e^(x+1)))/dx = e^(x+1)$

Returning from the digression:

$dy/dx = e^(x+1)$

How do you differentiate y=e^(x+1)+1y=e^(x+1)+1?