Math Is Fun Forum

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Could use some help with Derivatives of e^kx

Hi All.

I am trying to make my way through the definition for the derivative of

I can follow it fine until this part.

the next part has got me

i am not following how the k is taken out, it just seems to appear? The the k on the numerator is taken out of the fraction to give.

Should I review first principals before continuing?

Thanks

Dave

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Can feel it coming together.. Slowly but Surely

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Could use some help with Derivatives of e^kx

Hi DaveRobinsonUk.

I haven't learnt Latex yet so I'm having to explain this just with text, sorry.

If k is a constant (ie. not a variable like x) then it's ok to multply top and bottom by it, and to extract the top one outside the limit, as it isn't dependant on h.

Then I think there's an error, either in your post or in the text because the e in the limit should be to the power 'kh' not just 'h'.

Treat kh as if it was a single variable tending to zero.

Somewhere earler in the text you should have met that this limit  evaluates to 1, which makes the differential k times e to the kx, as required.

Does that help?  If not, I'll have to start learning how to do fancy scripts.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

DaveRobinsonUK

Member

Registered: 2010-04-24

Posts: 123

Re: Could use some help with Derivatives of e^kx

Hi Bob

yes sorry, the missing k is a typo on my part.

Thank you for the help, that has cleared things up for me.

Cheers
Dave

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Can feel it coming together.. Slowly but Surely

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Could use some help with Derivatives of e^kx

You're welcome.

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob