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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Chavi on September 28, 2010, 11:23:42 pm

Title: Implicit diff discrepancies
Post by: Chavi on September 28, 2010, 11:23:42 pm: Hey, whenever I come across a relation f(x,y) involving logs, I will always arrive at a different derivative depending on how I re-arrange the equation. Why is this so, and what mistake am I making?
For example:

"Find the gradient to the function $x\ln y + 2x^2 = 3$ at the point where $x=1$ "

When x = 1, y=e

Option 1
$\frac{d}{dx}(x\ln y + 2x^2 = 3)$
$\therefore \ln y + \frac{x}{y}y'+4x=0$
$\therefore y'=\frac{y}{x}(-4x - \ln y)$ P (1,e)
$\Rightarrow m=-5e$

Option 2
Rearranging gives: $\ln y = \frac{3-2x^2}{x}$
$\therefore \ln y = \frac{3}{x} - 2x$
$\therefore \frac{1}{y}y' = 3\ln x - 2$
$\therefore y' = y(3\ln x - 2)$
$\Rightarrow m = -2e$

According to the answers, option 2 is incorrect. Why is this so?
Title: Re: Implicit diff discrepancies
Post by: 98.40_for_sure on September 28, 2010, 11:32:17 pm: Because differentiaing 3/x is not 3lnx
Title: Re: Implicit diff discrepancies
Post by: Chavi on September 28, 2010, 11:46:08 pm: Quote from: 99.95_for_sure on September 28, 2010, 11:32:17 pm
Because differentiaing 3/x is not 3lnx
FML
Title: Re: Implicit diff discrepancies
Post by: sajib_mostofa on September 29, 2010, 12:01:17 am: How is option 2 correct if he has differentiated incorrectly?
Title: Re: Implicit diff discrepancies
Post by: m@tty on September 29, 2010, 12:26:55 am: Quote from: sajib_mostofa on September 29, 2010, 12:01:17 am
How is option 2 correct if he has differentiated incorrectly?

It isn't...
Title: Re: Implicit diff discrepancies
Post by: sajib_mostofa on September 29, 2010, 01:21:35 am: My bad, I read it incorrectly.