You need to remember that lnb is actually a number so the derivative of x lnb is just lnb because the derivative of x is 1 just like the derivative of 2x is 2
For the interval table at 6:32 since your intervals are (-∞,0) (0,2.9) (2.9, ∞) you can just use big numbers like x = -100 for (-∞,0) or x = 100 for (2.9, ∞) to make calculations so easy that it's just a matter of common sense. (of course you would have to do more thinking with the interval (0,2.9) though) just a little trick haha
not even in this class but I watched 2 mins of this video and it has already helped way more then my teacher has online lol thank you!! please keep up with grade 12 calc!
Happy to be of help to you! It's really tough to learn from a textbook and on your own. Feel free to ask questions if you are not understanding something.
And I would do anything to have such dedicated, polite and lovely students such as yourself! I loved being in the classroom and I still love the short interactions that I have with students all over the province. Thank you for the heartfelt message ❤️
All grade 11 functions classes are in the playlists as well as all the grade 12 advanced functions. Almost finished Calculus and Vectors. Tell all your friends to join the party 🎉 !! Thanks for commenting.
The reason is that in the numerator you have that nasty minus sign. So, if you were to factor an x out of the numerator you would have to take one x from both sides of it. So let's say that it was only ( x^2 - 2x) divided by x^4 in the numerator you would get x(x-2) if you factored out one x. Then you would take out the x from the top that you factored out and reduce the denominator by one to make it x^3 Does that help?
Hi Ms. Havrot. Would you be able to help me with some of my questions? I'm not sure how to do the inverse function of f. The function is given by f(x) = ln x/x+1 and the question is asking for a) the domain of f, b) the derivative of f at x=1 and lastly c) to write an expression for f^-1, where f^-1 denotes the inverse function of f. P.S. Your calculus videos and/or playlist are gold and it's helping me understand most of the aspects of the Calculus better than in class/online.
While working on the solution I came across this calculation socratic.org/questions/how-do-you-find-the-inverse-of-y-ln-x-x-1 It's pretty much what you are looking for (except it is (x-1) in the denominator. Also if you aren't familiar with this website it is awesome for finding derivatives www.derivative-calculator.net/
Ms Havrot, for students who do not major in Math, would you recommend trying understand the theory behind these formulas? I’m currently studying Calculus 1 on my own and it seems to me that it’s really just the manipulation of algebra and trigs as long as you know all the rules and formulas, but I wonder if I need to know where all these formulas came from.
It's always a good idea to have an understanding of the derivation of formulas. I always showed my students how formulas come about but never insisted that they be able to derive a formula on their own. Like you said, if you are going to MAJOR in mathematics there are courses that focus on this topic, but basically most students, even those in a science program, never need to derive formulas.
I’m not quite sure what you are asking but maybe this will help: when I say e^x we are using e = 2.71828.... (Euler’s number). And when we are using b^x, b can be any nonnegative number
That's a very good question. The short answer is yes, there is a difference. if y = lnx, y'= 1/x and if y = ln(f(x)) then y' = (1/x )(f'(x)) This is not part of the Ontario curriculum but I will cover it in my next lesson which will be based on the lesson in the appendix.
Thanks for the video. The exponential is way quicker and better than chain rule. I needed a video for revision, and this is perfect.
You’re welcome! Thank you for watching 😊
Thank you ever so much ! I loved not the lesson per se, but the way you taught it. With you Mrs Havrot Calculus makes sense !
That’s sweet of you to say ❤️
we did love it! thank you for redoing it 3 times, much appreciated
Hello Ms Havrot, what is the derivative of x·ln(b)? Why is the derivative of this ln(b)? Thank you!
You need to remember that lnb is actually a number so the derivative of x lnb is just lnb because the derivative of x is 1 just like the derivative of 2x is 2
@@mshavrotscanadianuniversit6234 Thank you Ms Havrot! :)
For the interval table at 6:32 since your intervals are (-∞,0) (0,2.9) (2.9, ∞) you can just use big numbers like x = -100 for (-∞,0) or x = 100 for (2.9, ∞) to make calculations so easy that it's just a matter of common sense. (of course you would have to do more thinking with the interval (0,2.9) though) just a little trick haha
Absolutely you can.
not even in this class but I watched 2 mins of this video and it has already helped way more then my teacher has online lol thank you!! please keep up with grade 12 calc!
Happy to be of help to you! It's really tough to learn from a textbook and on your own. Feel free to ask questions if you are not understanding something.
Yes, we loved it Ms Havrot! I wish you were still a teacher, because i'd do anything to attend the school at which you taught.
And I would do anything to have such dedicated, polite and lovely students such as yourself! I loved being in the classroom and I still love the short interactions that I have with students all over the province. Thank you for the heartfelt message ❤️
omg!!!!! GOD BLESS YOUR CHANNEL !!!!!!!!!!! PLEASE PLEASE keep posting more grade 11-12 videos. Thank you so much !!!!!! You are great !!!!!!!!!!
All grade 11 functions classes are in the playlists as well as all the grade 12 advanced functions. Almost finished Calculus and Vectors. Tell all your friends to join the party 🎉 !! Thanks for commenting.
@@mshavrotscanadianuniversit6234 of course will do !!!!!!!!!
thank you so much!! my phone died when my teacher was teaching this and was so confused by the time i got back.
Darn phones! Glad that you found help here. Lots of good lessons to supplement your teacher’s efforts and get you ready for university! 😊
Hell ms. Havrot, For Q5. could you explain how you canceled 2 x's from the top but reduced only one exponent from the bottom ?
The reason is that in the numerator you have that nasty minus sign. So, if you were to factor an x out of the numerator you would have to take one x from both sides of it.
So let's say that it was only ( x^2 - 2x) divided by x^4 in the numerator you would get x(x-2) if you factored out one x. Then you would take out the x from the top that you factored out and reduce the denominator by one to make it x^3 Does that help?
@@mshavrotscanadianuniversit6234 THANK YOU VERY MUCH 🙏❤
Hi Ms. Havrot. Would you be able to help me with some of my questions? I'm not sure how to do the inverse function of f.
The function is given by f(x) = ln x/x+1 and the question is asking for a) the domain of f, b) the derivative of f at x=1 and lastly c) to write an expression for f^-1, where f^-1 denotes the inverse function of f.
P.S. Your calculus videos and/or playlist are gold and it's helping me understand most of the aspects of the Calculus better than in class/online.
Is it the (ln x)/x+1 or ln (x/x+1)
@@mshavrotscanadianuniversit6234 The second one ln (x/x+1)
That makes it considerably easier! 🤣
While working on the solution I came across this calculation socratic.org/questions/how-do-you-find-the-inverse-of-y-ln-x-x-1 It's pretty much what you are looking for (except it is (x-1) in the denominator.
Also if you aren't familiar with this website it is awesome for finding derivatives www.derivative-calculator.net/
@@mshavrotscanadianuniversit6234 Oh Thank you so much.
Ms Havrot, for students who do not major in Math, would you recommend trying understand the theory behind these formulas?
I’m currently studying Calculus 1 on my own and it seems to me that it’s really just the manipulation of algebra and trigs as long as you know all the rules and formulas, but I wonder if I need to know where all these formulas came from.
It's always a good idea to have an understanding of the derivation of formulas. I always showed my students how formulas come about but never insisted that they be able to derive a formula on their own. Like you said, if you are going to MAJOR in mathematics there are courses that focus on this topic, but basically most students, even those in a science program, never need to derive formulas.
i just dont know when to use y=e^x and y=b^x. like when should i use what. please help :(
I’m not quite sure what you are asking but maybe this will help: when I say e^x we are using e = 2.71828.... (Euler’s number). And when we are using b^x, b can be any nonnegative number
how would we differentiate a function with lnx in it? would there be a difference?
That's a very good question. The short answer is yes, there is a difference. if y = lnx, y'= 1/x and if y = ln(f(x)) then y' = (1/x )(f'(x)) This is not part of the Ontario curriculum but I will cover it in my next lesson which will be based on the lesson in the appendix.