Help me find derivatives

[Omegachi]

can any one help me find the 1st and 2nd derivative of

117e^(-10/x)

THen can you solve for X for both of the deriv...

 

[bolomite]

So you have f(x)=117e^(-10/x). Looks like a function of the form Ae^u, where u=(-10/x). Since the deriv. of e^x is itself, the deriv of e^u is e^u (du/dx) via Chain Rule.

I get f'(x)= 117e^(-10/x)(10/(x^2)), where the second parentheses is from Quotient Rule on the 'u' part.

Cleaning up yields f'(x) = (1170/(x^2)) e^(-10/x) Hopefully I didn't goof 😀

A characteristic of exponential fcns. is that when you differentiate, the e raised to the whatever part appears in the derivative, and some extra junk is created also, in the form of additional terms out in front.

To find f ' ', I think it's more involved. If you look at the first deriv. compared to the original function, the term out in front now has x in it, where before it was just a constant. So, you'll have to use Product Rule to differentiate, with the two parts (1170/(x^2)) and e^(-10/x) as your f(x) and g(x). And that gets hairy.

As for solving, well what are the derivatives set equal to? Zero? Some other constant? It just becomes an algebraic exercise.