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Logarithm derivation proof

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
Chain rule.
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davros
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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 eu=xe^ u = x.

Then the chain rule tells you that

d(eu)dx=eu⋅dudx\dfrac{d(e^u)}{dx} = e^u \cdot \dfrac{du}{dx}

So what can you deduce about dudx\dfrac{du}{dx}?

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