Year 12s: what will be the first way you research your future options? >>

Differntiation of ln 1/x

mh1985

Hi can someone please help with this, I've got a different answer to what I'm supposed to.

y= ln \frac{1}{x}= ln x^{-1}

\frac{dy}{dx} = (\frac{1}{x^{-1}})( -1x^{-2})

=\frac{-1x^{-2}}{x^{-1}}

The answer is supposed to be

-1\frac{1}{x}

according to the book but I can't see how they got it.

Reply 1

didgeridoo12uk

y = ln(x^{-1}) = -ln(x)

start it off like that, its easier

also your answer is identical to the one they've given

\frac{-1x^{-2}}{x^{-1}} = -1 \frac{1}{x^{2}} \frac{1}{x^{-1}} = -1 \frac{1}{x}

(edited 13 years ago)

Reply 2

dnumberwang

that's the same as what you got

Reply 3

Jing_jing

Original post by mh1985

Hi can someone please help with this, I've got a different answer to what I'm supposed to.

y= ln \frac{1}{x}= ln x^{-1}

\frac{dy}{dx} = (\frac{1}{x^{-1}})( -1x^{-2})

=\frac{-1x^{-2}}{x^{-1}}

The answer is supposed to be

-1\frac{1}{x}

according to the book but I can't see how they got it.

Try simplifying your answer

Reply 4

Legit

Original post by mh1985

Hi can someone please help with this, I've got a different answer to what I'm supposed to.

y= ln \frac{1}{x}= ln x^{-1}

\frac{dy}{dx} = (\frac{1}{x^{-1}})( -1x^{-2})

=\frac{-1x^{-2}}{x^{-1}}

The answer is supposed to be

-1\frac{1}{x}

according to the book but I can't see how they got it.

x^-2 / x^-1 = x^-1
Cause its -2 - (-1) = -1

so your left with -1(x^-1)
= - 1/x

Reply 5

IchiCC

Original post by mh1985

Hi can someone please help with this, I've got a different answer to what I'm supposed to.

The answer is supposed to be

according to the book but I can't see how they got it.

What you've done is correct, you just haven't simplified your answer fully. Try multiplying both the numerator and denominator by

x

.

A faster way of approaching the problem would be to observe that

ln(\frac{1}{x})=-ln(x)

, and going from there.

Quick Reply

Latest

Articles for you

Bmat: when it is, what it costs and how to prepare

Edexcel A-Level Economics Paper 1 - Unofficial Mark Scheme - 18 May 2023

What is an LLM and how could it benefit your career?

Powerful questions business students forget to ask their career advisers

Differntiation of ln 1/x

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you