## anonymous 4 years ago y=d/dx integralcosx to 0 t/(1+t)dt

1. anonymous

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

2. anonymous

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

3. anonymous

how did u do it?

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

|dw:1349804491261:dw|

9. anonymous

Now take the derivative

10. anonymous

it shouldn't be anything @ zekarias

11. anonymous

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

12. anonymous

What u get finally?

13. anonymous

so the answer is just cosx/1+cosx ?

14. anonymous

yes

15. anonymous

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

16. anonymous

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. anonymous

oh thanks alot sweedy :)