its been forever since my calc 1 class...?

Question

so i took calc 1 when i was a senior in high school and im a junior in college now...so i've forgotton some of the differentiation rules... my question is, when you differentiate e^x the answer is e^x, but what if you are differentiating e^(1/x)? do you follow the rule where you have d a^x/dx =ln(a)*a^x? Thanks!

Answer 1

you use the chain rule of differentioan

let u = 1/x

d/dx( e^(1/x) ) = d/dx( e^u)
= d/du(e^u) du/dx
= e^u d/dx(1/x)
= e^(i/x) (-1/x^2)
= - e^(1/x) / x^2

Answer 2

a) enhance functionality (year) = 6,seven hundred,000,000(a million.012)^(year – 2007) b) inhabitants in 2020 is expected as 6,seven hundred,000,000(a million.012)^thirteen = 7,823,867,one hundred ten this is going to be rounded to 7.8 billion to verify enter accuracy.

Answer 3

derivative of e⁻ⁿ =
e⁻ⁿ (-n⁻²)
use chain rule on exponent of e.