Author Topic: urgent please help me to differentiate (Read 1646 times) Tweet Share

destain · « **on:** May 17, 2012, 08:12:07 pm »

Firstly i want to know if you can use the quotient rule to differentiate if there is only a variable on the denominator and secondly how do i differentiate this using calculus... i have to show it

x/1.8 + root( x^2 - 200x + 12500)/1.2

How do i differentiate something like this...
and in general, the best way to differentiate fractions whether or not there is a variable on both the nnumber and denominator or just one of the two

Phy124 · « **Reply #1 on:** May 17, 2012, 09:16:31 pm »

Quote from: destain on May 17, 2012, 08:12:07 pm

Firstly i want to know if you can use the quotient rule to differentiate if there is only a variable on the denominator and secondly how do i differentiate this using calculus... i have to show it

x/1.8 + root( x^2 - 200x + 12500)/1.2

How do i differentiate something like this...
and in general, the best way to differentiate fractions whether or not there is a variable on both the nnumber and denominator or just one of the two

As the denominator is only a number, you can just use the chain rule.

*Note: Some of the things I show below aren't necessary I'm just doing so that it may be easier to interpret.

For $\frac{x}{1.8}$

$\frac{x}{1.8}=\frac{1}{1.8}x$

$\therefore \frac{d}{dx}\frac{x}{1.8}=\frac{1}{1.8}$

For $\frac{\sqrt{x^2-200x+12500}}{1.2}$

$\frac{\sqrt{x^2-200x+12500}}{1.2}=\frac{1}{1.2}\sqrt{x^2-200x+12500}$

$Let \ y = \frac{1}{1.2}\times\sqrt{u}$

$\frac{dy}{du}=\frac{1}{1.2}\times \frac{1}{2\sqrt{u}}=\frac{1}{2.4\sqrt{u}}$

$Let \ u = x^2-200x+12500$

$\frac{du}{dx}= 2x - 200$

$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}=\frac{1}{2.4\sqrt{u}}\times (2x - 200)=\frac{2x - 200}{2.4\sqrt{u}}=\frac{2x - 200}{2.4\sqrt{x^2 -200x + 12500}}$

Add the two together

$\frac{dy}{dx}=\frac{2x - 200}{2.4\sqrt{x^2 -200x + 12500}}+\frac{1}{1.8}$

destain · « **Reply #2 on:** May 17, 2012, 09:56:38 pm »

uhm and to make that = to 0 and solve for x what would i do?

pi · « **Reply #3 on:** May 17, 2012, 10:09:03 pm »

Hit the CAS

destain · « **Reply #4 on:** May 17, 2012, 10:12:41 pm »

well i have a sac soon and i know theres a question which is like that without cas you ahve to show via calculus

Phy124 · « **Reply #5 on:** May 17, 2012, 10:35:59 pm »

Quote from: destain on May 17, 2012, 10:12:41 pm

well i have a sac soon and i know theres a question which is like that without cas you ahve to show via calculus

If the $\frac{x}{1.8}$ wasn't apart of the equation then you could do it by hand. (The denominator of the derivative would "disappear" when multiplied across and you would be left with 2x-200, x = 100). But as long as that stays, I don't think you'll be solving that by hand

destain · « **Reply #6 on:** May 17, 2012, 10:48:34 pm »

okies thank you hope the question will be like that!

ecvkcuf · « **Reply #7 on:** May 18, 2012, 08:18:37 pm »

yer destain.. my school is doing a similar sac.. it's all cas.. and it's 6 hours..

how many hours is the mhs one? it's analysis btw..

destain · « **Reply #8 on:** May 23, 2012, 03:49:02 pm »

idk just 3 periods of project and 2 of tests

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Author Topic: urgent please help me to differentiate (Read 1646 times) Tweet Share

destain

urgent please help me to differentiate

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destain

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Phy124

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