Evaluate limit again..

Question

anonymous · Answer

the answer is 2/7777 but i cant get that

anonymous · Answer

i know wee need to use L'hopitals rule but how do u differentiate $$\int\limits_{36}^{x^2}\frac{ 1 }{ 1+t^\frac{ 5 }{ 2 } }dt$$

hartnn · Answer

still need help with this ? @ememlove

anonymous · Answer

yes plssss.. haha @hartnn

hartnn · Answer

using the chain rule, it'll be 
$\huge \dfrac{1}{(1+x^2)^\dfrac{5}{2}}\times \dfrac{d}{dx}x^2$

did u get how ?

anonymous · Answer

why can we use chain rule here when it is a fraction?

hartnn · Answer

i meant 
$\huge \dfrac{1}{1+(x^2)^\dfrac{5}{2}}\times \dfrac{d}{dx}x^2$

hartnn · Answer

we needed to use the chain rule bcause the upper limit was NOT 'x'
it was some function of 'x' , here x^2

hartnn · Answer

so if it were like 36 to log x, then you would have multiplied it by d/dx of log x

anonymous · Answer

ah, i see.. so we shd always use chain rule if the upper limit is some function of x?

hartnn · Answer

yes!

anonymous · Answer

what if it was x, and not x^2?

hartnn · Answer

then you would multiply nothing (or d/dx (x) which =1)
and it'll be just 
1/1+(x)^5/2

anonymous · Answer

ahhh... okay okay i get it now, haha thank you! :D

hartnn · Answer

welcome ^_^