## krypton 3 years ago y=d/dx integralcosx to 0 t/(1+t)dt

1. krypton

$d/dx \int\limits_{0}^{cosx} \frac{ t }{ 1+t } dt$

2. Outkast3r09

$\frac{cosx}{1+cosx}$

3. krypton

how did u do it?

4. Zekarias

@Outkast3r09 I think u made a miss take in your first step (While u made the integral)

5. Outkast3r09

the derivative of an integral is simply the integral itself with the variables in other words ... integrals and derivatives cancel eachother out

6. Outkast3r09

$\frac{cosx}{1+cosx}$is your answer

7. Zekarias

It should be$\cos(x)-\ln(1+\cos(x))$

8. Outkast3r09

|dw:1349804491261:dw|

9. Zekarias

Now take the derivative

10. Outkast3r09

it shouldn't be anything @ zekarias

11. Outkast3r09

@zekarias ... you don't need to do anything

12. Zekarias

What u get finally?

13. krypton

so the answer is just cosx/1+cosx ?

14. Outkast3r09

yes

15. krypton

thanks,wolfram gives me the same answer,just wanted to make sure how it was done

16. Outkast3r09

it's just simply knowing how an integral work... there is a lot of work to do it zekarias way but if you just know that the the derivative on an integral will bring you back to the f(x) within the integral... that's all you need to know(This works anytime the lower limit is some real number) because if you think about it.... |dw:1349804918350:dw| if you take the derivative of f(n)... you'll always get zero

17. krypton

oh thanks alot sweedy :)