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Delos · Aug 18, 2009, 07:07 AM

Hi,

Can someone please tell me how to differentiate this particular formula with step by step direction?

A= 2n * (1/2) * (150/n) * [ (150/n) / tan (180/n) ]

Thanks in advance. As soon as possible if you can :)

Delos · Aug 18, 2009, 07:32 AM

Oops forgot to simplify tehe

A= (300n/2n) * [ (150/n) / tan (180/n) ]

Unknown008 · Aug 18, 2009, 07:48 AM

You should be simplifying your equation first, further than what you've done:

$\begin{eqnarray}A &=& \cancel{2n} \times \frac{1}{\cancel{2}} \times \frac{150}{\cancel{n}} \times \[\frac{\frac{150}{n}}{tan(\frac{180}{n})}\] \\ &=& 150 [ \frac{150 tan(\frac{180}{n})}{n}] \\ &=& \frac{22500tan(\frac{180}{n})}{n}\end{eqnarray}$

Now use the quotient rule to differentiate:

If $y = \frac uv$

then.

$\frac{dy}{dx} = \frac{v.\frac{du}{dx} - u.\frac{dv}{dx}}{v^2}$

Delos · Aug 18, 2009, 08:20 AM

Hey thanks for the response. One question though, why did you put the tan (180/n) up? I don't that part.

Unknown008 · Aug 18, 2009, 08:34 AM

I prefer dealing with simple fractions as far as possible. You can use the quotient rule, but to get less confused, putting it up is better.

If you're asking me if that's possible, then yes;

$\frac{2}{$\frac12$} = 2 \div \frac 12 = 2 \times \frac 21 = \frac{2 \times 2}{1}$

galactus · Aug 18, 2009, 05:20 PM

Be careful.

$\frac{\frac{22500}{n}}{tan(\frac{180}{n})}=\frac{2 2500}{ntan(\frac{180}{n})}\neq \frac{22500tan(\frac{180}{n})}{n}$

$=\frac{22500cot(\frac{180}{n})}{n}$

If that were $\frac{1}{tan(\frac{180}{n})}$ in the denominator, then that would be OK.

Unknown008 · Aug 19, 2009, 08:44 AM

Oh, sorry... I my head was not completely on that thread... :( Thanks galactus for correcting me.