Question

What's the derivative of ln(e^(dx)+k), assuming that d and k are constants. Thanks!

Answer 1

Given something of the form \(\ln(\text{inside})\), its derivative is \(\dfrac{(\text{inside})'}{(\text{inside})}\).

Here, \(\text{inside}=e^{dx}+k\).

Answer 2

So would it be ((e^(dx)+1)/(e^(dx)+k)?

Answer 3

your denominator is correct, but what about the derivative of inside = e^dx+k ??

Answer 4

Don't I differentiate the derivative of the inside, so derivative of e^dx and the derivative of k. Derivatives of e is itself isn't it? And since k is a constant, it'd be 0?

Answer 5

yes, derivative of k is 0, (you have written 1 there instead)

and derivative of e^x is e^x, yes.

but derivative of e^dx will be d*e^dx
because we multiply by the co-efficient of x, because of chain rule.
d/dx (e^dx ) = e^dx * d/dx (dx) = e^dx *d
understand ?

Answer 6

Yeah I just realized that as I was replying, sorry. But thanks a lot! I get it now :)

Answer 7

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Answer 8

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Answer 9

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