Correction check on this please ?

[Mathmasteriw]

Hi Guys and Gals,
I have a load of calculus to do, can anyone tell me if im correct / on the right track with this?
Thanks ?

 

[Steven G]

In your next to last line you wrote that you needed to multiply by cos(u) but in the last line you multiplied by sin(u). Yes you plugged in the correct u, but you wrote sin instead of cos.

You also have the wrong result for du/dx. Try computing that again.

 

[Steven G]

You also wrote Asin(x) = Acos(x). Why do you think that is true?

 

[Dr.Peterson]

I think Jomo meant that du/dt is wrong.

One thing that will help a lot is to stop writing x where there is no x. It appears that x is used in your derivative formulas; but that is just a placeholder for any variable. In your work, v = sin(u), so that's the variable you should use: dv/du = cos(u). (You also don't need to write the A from the formula; that has been replaced by 1 here.)

 

[Mathmasteriw]

Thank you guys so much! Will try again on a clean sheet of paper

 

[Mathmasteriw]

You also wrote Asin(x) = Acos(x). Why do you think that is true?

 

[Mathmasteriw]

View attachment 24181

Mabey i shouldn't of used ' = ' but this is where it came from

 

[Mathmasteriw]

Heres what I have now,
Dose this look correct?
Thanks for your time guys ?

 

[Dr.Peterson]

There are some notation issues, and some slips in the work itself. Here is an annotated copy of your work:



The proper notation is that [MATH]\frac{d}{dx}A\sin(x) = A\cos(x)[/MATH], so in particular [MATH]\frac{d}{du}\sin(u) = \cos(u)[/MATH]. It is not true that [MATH]\frac{dv}{du}=A\sin(u)[/MATH], but rather [MATH]\frac{dv}{du}=\cos(u)[/MATH].

Now fix that [MATH]\frac{du}{dt}[/MATH]!

 

[Mathmasteriw]

Doh!! Sorry i think i was in auto-pilot mode when writing that last question! Now i realise i havent corrected any of the mistakes previously pointed out ?
Back to it tomorrow! Thanks so much for the help

 

[Mathmasteriw]

right guys , im really stuck here dont know how to get this to the next step ? whats the rule to use?
I have circled it i blue in the attached photo
??

 

[Harry_the_cat]

On your rule sheet, the rule you need to use is on the line above the one you circled in red.

 

[Deleted member 4993]

right guys , im really stuck here dont know how to get this to the next step ? whats the rule to use?
I have circled it i blue in the attached photo
??View attachment 24229

use the 1st. rule of your rule sheet. If:

u = 2 *t^3 + 4*t - 2

du/dt = ?

 

[Mathmasteriw]

so.... 2*t^3 + 4*t -2
du/dt = 10t -2 ????

 

[Deleted member 4993]

so.... 2*t^3 + 4*t -2
du/dt = 10t -2 ????

NO!

Can you rewrite the first rule here - please!

 

[Mathmasteriw]

Ax^n nAx^n-1. this one????

 

[Harry_the_cat]

Ax^n nAx^n-1. this one????

yes

 

[Mathmasteriw]

A ok so use this rule to simplify this line? ok got ya thank you so much for your time

 

[Harry_the_cat]

So if \(\displaystyle u= 2t^3+4t -2\) then \(\displaystyle \frac{du}{dt}= \) ??

 

[Deleted member 4993]

Ax^n nAx^n-1. this one????

Yes....