What is the derivative of \frac{1}{\log x}?

Kathleen Rausch

Kathleen Rausch

Answered question

2021-12-13

What is the derivative of 1logx?

Answer & Explanation

Virginia Palmer

Virginia Palmer

Beginner2021-12-14Added 27 answers

It is 1x(logx)2(ln10) (Assuming that logx=log10x
Explanation:
The function f(x)=1logx
is of the form: f(x)=1u=u1
So we find its derivative using the power rule and the chain rule:
f(x)=1u2dudx=1u2dudx
In this case, u=logx  which I take to mean  log10x
The derivative of logbx=1xlnb,  so we have:
dudxddx(logx)=ddx(log10x)=1xln10
Putting this together, we get:
f(x)=1(logx)21xln10=1x(logx)2(ln10)
Note: If we are using logx for the natural logarithm (as is sometimes done), then, that would be logex and natural log of e is 1 , so we get
f(x)=1(logx)21x=1x(logx)2
Natalie Yamamoto

Natalie Yamamoto

Beginner2021-12-15Added 22 answers

Wow, cleverly you came up with it, I didn't even understand at the beginning, well done

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