# Logarithm derivation proof

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#1
By differentiating both sides of exp(log x) = x, show that the derivative of log(x) is 1/x.

Hi everyone,

Any thoughts on the above question? I had a go but the problem I faced was that when you differentiate both sides of exp(log x) = x, you get 1 on both sides. I don't understand how you are supposed to do this. Can anyone please help me?

Thanks
0
4 weeks ago
#2
Chain rule.
0
4 weeks ago
#3
(Original post by Oakenari)
By differentiating both sides of exp(log x) = x, show that the derivative of log(x) is 1/x.

Hi everyone,

Any thoughts on the above question? I had a go but the problem I faced was that when you differentiate both sides of exp(log x) = x, you get 1 on both sides. I don't understand how you are supposed to do this. Can anyone please help me?

Thanks
To expand on the above hint...

Write u = log x so that .

Then the chain rule tells you that

So what can you deduce about ?
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