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anonymous
 4 years ago
James?
anonymous
 4 years ago
James?

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh that was annoying i cldnt type

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0give me medals free medals for everyone

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0can you write the equation again please :D

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4\[ \frac{d \ }{dx} \int_{17}^x \sin(t^2)/t \ dt \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0d/dx(sinx^2/x)  d/dx(sin(17)/17)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0where did i go wrong?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4look at the earlier example with ln

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0wasn't it d/dx(F(x)F(17))

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh i see where i went wrong!!!!

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4Yes, but F is not the integrand.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0K just tell me the answer

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4Look at the ln example again.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0In the example we subsituted t for x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0In the example we subsituted t for x

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4\[ \frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4What is the value of that expression?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i dont know i am feeling very stupid!!!!!! dF/dx=ln(x^2+1)

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4If \[ F(t) = \int \ln(t^2+1) \ dt \] then \[ \int_2^x \ln(t^2+1) \ dt = F(x)  F(2) \]. Hence \[\frac{d \ }{dx} \int_2^x \ln(t^2+1) \ dt = \frac{d \ }{dx} (F(x)  F(2)) \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4and by the Fund Theorem of Calculus, dF/dx = ln(x^2 + 1). Also (d/dx)F(2) = 0 because F(2) is a number, a constant. Hence the entire expression is just ln(x^2+1)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0James do you think you help me please?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4So, return now to the next example where the integrand has a sin function. What is the value of that derivative?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4@mft, I'll try and get to it. unfortunately you're not the first to ask.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dont take james away form me:(

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4quick rld613. I want to move on with you to yet another example afterwards

Hero
 4 years ago
Best ResponseYou've already chosen the best response.0rld said she didn't need OS anymore

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4so (d/dx) int_17^x sin(t^2)/t dt = ...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i didnt get that why is 17 to th epower of x

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4\[ (d/dx) \int_{17}^x \sin(t^2)/t \ dt \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4evaluate. What is the that equal to.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0y is it wrong what i showed u b4?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0plz be nice to me and show me all the step? :D

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4No. You write out the steps, following line by the line the example we just used for ln. I'm going to help someone else for a while and expect the right answer when I get back ;)

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4I'm serious. And I'll be back in 5 minutes, so hurry.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0u did u come back already!!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0K can u walk me thru the steps cuz like i bever learnt this stuff? YOu r so scary LOL

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I was hoping i wld have the answer b4 u wld return

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0teh answer wld sinx/x?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4Exactly as before, exactly, let \[ F(t) = \int \sin(t^2)/t \ dt \] Then \[ \int_{17}^x \sin(t^2)/t \ dt = F(x)  F(17) \] Thus the derivative of this definite integral \[ \frac{d\ }{dx} (F(x)  F(17)) = ... \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0iSo what is F(x)?????

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That is where i am going wrong

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4like we've seen, we actually don't need an explicit formula for F(x). We just need to know it is this integral and then use the Fundamental Theorem of Calculus.

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4What is dF/dx here? What is it equal to?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4By the FTC, dF/dx = .... what?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You are forsure ready to kill me!!!!!!!!!!!!!!!

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0You are forsure ready to kill me!!!!!!!!!!!!!!!

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4correct. Hence the derivative wrt (with respect to) x of the entire integral equals what?

pokemon23
 4 years ago
Best ResponseYou've already chosen the best response.1hey james can you help me with math?

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4This thing ... what's it equal to?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sinx^2/x????? this is a guess

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4it shouldn't be guess. it is exactly right.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That is what i thought in the first place but i left out by accident the squared

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I can be so annoying sometimes

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4Now one more to make sure you really understand. Evaluate this: \[ \frac{d \ }{dx} \int_x^{x^2} \sqrt{t^3+1} \ dt \]

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4Now write out the steps. This problem isn't exactly the same as the others.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[d/dx=(\sqrt{x ^{6}+1}\sqrt{x ^{3}+1})\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I think it was suppossed to be dF/dx

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4The expression is equal to \[ \frac{d \ }{dx} \left( F(x^2)  F(x) \right) \ \ \ \ \ \ (*)\] where by the Fund Theorem of Calculus, \[ dF/dx = \sqrt{x^3+1} \] Now given that, evaluate the first expression, (*).

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4hint: you need to use the chain rule.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so let me try that

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0james u gotta help me out on this one

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4you think about it for a bit and write the answer sometime in the next day when you know what's going on.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0alrighty thanks james

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I will call you back when i get the

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[2x \sqrt{x ^{6}+1}  \sqrt{x ^{3}+1}\] Here is my answer. Thanks james for your help. I really appreciate it

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4One more variation they might throw at you in the exam. Evaluate: \[ \frac{d^2 \ }{dx^2} \int_2^x \ln(\cos t) \ dt \]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Oh this is very simple there is just one small catch that you have to differentiate it twice

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0d/dx(ln(cosx)) (1/cosx)*sin(x)= sin(x)/cos(x) tan(x)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I think that is the answer. I took my final exam already and it was basically simple except ofr a related rates problem. Going on vacation for a month So see u then. Thanks for your help james

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Thanks for helping me out

JamesJ
 4 years ago
Best ResponseYou've already chosen the best response.4sure. have a good vacation.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0U better take a vacation from OS tooo!!! :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ya u need a break to refresh again

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0OS wldnt survive without James myinaya satellite and Hero
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