Dx/x of quotient by def of derivative

[karush]

Homework Statement

ok I am retired just doing some review problems

Relevant Equations

definition of derivative

$f(x)=\dfrac{x^2-1}{2x-3}$
ok I just don't see any preview so don't want to add more...

 

[PeroK]

Homework Statement: ok I am retired just doing some review problems
Relevant Equations: definition of derivative

$f(x)=\dfrac{x^2-1}{2x-3}$
ok I just don't see any preview so don't want to add more...

You need two dollar signs to delimit your Latex:$$f(x)=\dfrac{x^2-1}{2x-3}$$

 

[karush]

double \$\$ centers the latex which I don;t want other forums only require one $ wrap $
besides it didm"t render in the preview with double \$\$

anyway this we are supposed to solve by means of def of a derivative which can get quite involved

$$f'( x)=\displaystyle\lim_{h \to 0} \dfrac{{f(x + h)-f(x)}}{h}$$

 

[berkeman]

anyway this we are supposed to solve by means of def of a derivative which can get quite involved

You need to take the derivative using the original definition, instead of just using the quotient rule for derivitaves?

 

[karush]

$$f'(x)=\displaystyle\lim_{h \to 0}
\dfrac{\dfrac{(x+h)^2-1}{2(x+h)-3}-\dfrac{x^2-1}{2x-3}}{h}$$
my first inclination is to expand the numerator and combine the fractions

 

[PeroK]

$$f'(x)=\displaystyle\lim_{h \to 0}
\dfrac{\dfrac{(x+h)^2-1}{2(x+h)-3}-\dfrac{x^2-1}{2x-3}}{h}$$
my first inclination is to expand the numerator and combine the fractions

What else is there to do? Combine, simplify, cancel a factor of $h$ (hopefully) and get a simple limit to evaluate.

 

[PeroK]

double \$\$ centers the latex which I don;t want other forums only require one $ wrap $
besides it didm"t render in the preview with double \$\$

anyway this we are supposed to solve by means of def of a derivative which can get quite involved

$$f'( x)=\displaystyle\lim_{h \to 0} \dfrac{{f(x + h)-f(x)}}{h}$$

It's two hashes for inline Latex.

You can't preview Latex on the first post. It's just the developers showing who's boss.

 

[Ibix]

double $$ centers the latex which I don;t want other forums only require one $

One dollar sign is a bad choice for $\LaTeX$ delimiters in forums, because people quite frequently want to say things like "it was $2 for one and $3 for two" and you don't want that to render $\LaTeX$. So, as others have noted, it's two # for inline maths and two $ for paragraph maths.

The parser here has three oddities, as far as I know because (as much as we love it here) it's a minority-interest add-on to standard forum software. First, it won't render unless there is already $\LaTeX$ on the page - a page refresh cures this. Second, it won't render in preview if there isn't already $\LaTeX$ on the page - a page refresh while in preview mode cures this (the wise poster takes a copy of their text before refreshing). Third, it won't render at all in the new thread preview - I just prepare a thread start as a reply to a random thread that uses $\LaTeX$ and copy-paste into the new thread page when I'm ready.