What do I do with my e's?!! Maths Question

dmg24

Hi guys,

Nearly at the end of my course, but missing a load of notes still so asking for a little help.

I have the following question:

Find the gradient of the curve with equation y = 5e^3x + 2e^-x at the point where x = 0.

Now I'm ok just with x's and how to find the gradient once I have the equation, but what do I do to those nasty e's?!!

Thanks chaps! x

dmg24

Just to add, I've got 13 as the answer, but that could be rubbish! x

Blacksheep1979

If I remember right the differential of e^x = e^x therefore

if you let u = 3x and v = -x

dy/dx = du/dx * 5e^u + dv/dx * 2e^v

= 15e^3x - 2e^-x

if x = 0 then yes the answer would be 13 - but it is 10 years since I last properly did anything along these lines.

dmg24

Star - thanks Blacksheep! x