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[dejan91]

Let the function have a rule , where . Let be another continuous function with domain . For all real values of , what will the derivatives of be equal to?

The answer is  .

 I don't get the worked solutions when it says: let . Why suddenly introduce log?

[tl]

Umm... is that the entire question?

[dejan91]

It was multi-choice:

A

B

C

D

E

[TrueTears]

one function is the other function is

We require

Thus let and



1.

Thus

2.

Thus overall

This question is way beyond Methods, in Methods you don't need to derive exponentials except for e.

[kamil9876]

I don't get the worked solutions when it says: let a^{x} = e^{kx} : log_{e}(a^{x}) = kx . Why suddenly introduce log?

this is the definition of logarithm, inverse function of exponential.

Personally I would just make the subsitution:

let so that I can differentiate. They probably tried to do the same thing.

[dejan91]

This question is way beyond Methods, in Methods you don't need to derive exponentials except for e.

I wasn't expecting that from Neap! :O

kamil9876, I think they tried the first way you mentioned, beacause another part of the solution was exactly what you had there with the kx.

[TrueTears]

Yeah kamil's way is pretty good, but for Methods sake, if you see questions where the base is not e and you want to derive it, just make it to the base e by some manipulation.