Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Derivatives - Quotient and Chain Rule and Simplifying - One complete example. For more free math videos, visit PatrickJMT.com
For all who don't know, he cancels the 1/2 and the 2 because of the chain rule. When you have the chain rule, you multiply the power you brought down with the derivative of inside function. In this case, 1/2 x 2 = 1 or just x. You're welcome.
I have a test in business calculus tomorrow and I couldn't understand combining the chain rule and product/power rules for the life of me. Now I have a chance, so thank you so much.
Thank you so much for this. Out of nowhere, my professor said we needed to simplify these for our exam....when on the HW we didn't need to. You're a life saver
OHMYGOSH I DONT KNOW HOW I CAN THANK YOU! I'm a really bad procrastinator and I have a test tomorrow. I didn't get how to simplify the derivatives, so I thought that I would fail tomorrow's test. You are a life saver! Thank you so much!!!! Thank you thank you thank you!. Omygosh the feeling you get when you finally understand how to do somehting! It's such a wonderful feeling. Thank you!
In our AP Calculus class, we were taught a bit more humorous (and catchier) way of remembering the formula for the Quotient Rule. We learned it as: HoDhi-HiDho/ HoHo Where: Ho - Denominator (Ho rhymes with "low") Hi - Numerator (Hi is just..."high") Dho - Derivative of "ho" (D=Derivative) Dhi - Derivative of "hi" It just sounds a bit better that the formal way, and it's a pretty good brain trick to memorize it. It sounds pretty cool to say, as well, like a song. ^_^
Quotient Rule: (f/g)' "low d high - high d low/ over the square of what's below" xD This another way how I learned to memorize the quotient rule theorem...a song lol the d stand for the derivative. I just wanted to share that with you! You're videos are great btw! It's been helping me through my calculus and trigonometry (:
One out of ten videos I watched addresses the inside function thing (and that's yours). Wanted to C if I was doing it right. Thanks! Old videos are great! June 2022.
well, if the discriminant is negative, it means that the quadratic will not factor into the product of two linear factors with real roots... so that is about as simplified as it would get! (using real numbers)
Thank you so much. I had the product, quotient, and chain rules down, but when you put them together I had no idea what to do. I have a test over this tomorrow and this has helped me understand so well.
I cant believe i wasted hours asking this question on chegg and searching other stuff on google just to finally find your video and know what to do. I couldve gotten my assignment done like 5 hours ago and now i feel dumb for not finding this sooner
Thanks, Patrick. You saved my hind for algebra. You got me through trig. And now you're helping my way through physics and calculus. Great videos. I'd like to see a blackboard with neon markers... But that's just me. Hah.
Thanks alot ,you saved my life , your methods are simple and easy to understand i hope you increase the amount of the examples and make them total 5 everything is perfect beside that
he just took out the smaller power that was -1/2 and then inside the bracket he left( x^2+5 )^1 soo that ....1 + (-1/2) = 1/2 ...that will give the same result soo even after taking out the different exponent -1/2 we will get the same result that was 1/2 hope u understnd wht i was trying to clarify here all the best cheers:)
There was a part in here where you simplified the fractions. I do not know if that is the exact name for it. But I am referring to the part where you simplified an equation to the third power from an equation to the fourth power and added the equation to the fourth power again. If you watch your video again, (I am talking about the part where the time is at 3:32). Can you explain this a little further. I am lost.
I get the moving the terms with negative exponents down part. But how would you simplify something like x^-1/2 + y^-1/2 divided by x^1/2 + y^1/2? I can’t just move the numerator down because it’s 2 terms. How would I be able to simplify something like this?
Patrick , I'm curious about your view on why so many students claim to not be able to grasp what is taught in the classroom. Surely most math teachers are quite good at explaining.
@chupakabra you can just do this: square the bottom. take the product rule with a minus sign on top and then multiply times a negative sign. it would be like -(f g'-g f')
You have explained better then my professor , while your were explaining i know that you know what you're doing , unlike my proff i can see through her that shes getting rekt by teaching
After you have factored everything and you are simplifying the numerator, say g(x) with exponent -1/2 has a number in front of the term, is that number brought down to the denominator as well or is it left in the numerator? So say it was 2(x^2+5)^-1/2...what would happen to the 2? Thanks
The 2 would go at the top. This is because only the terms in the parentheses are being multiplied by the negative exponent. So, only the terms in the parentheses would go in the denominator.
Isn't it possible to just use the product rule for division instend of having to remember two formulas or working with the trickier quotient rule. I think I read somewhere about that but I can't remember where.
Hi, i was just wondering. What if we move the denominator instead having the numerator goes down. I did this, so am i correct or nah? Just like at 5:03 nut revrese instead the denominator goes up plus i uses product rule sk there's no denominator as if is implified the function
Can you please explain more on how you simplify and factorise.. i don't get how 1/2 cancels out 2x etc and why you pull out the x... can you say why you do instead of just doing it. thanks
At 02:34 he said the 1/2 x 2 make it disappear. Now when he rewrite the clean equation, the 1/2 that was attached to the (x2+5) disappeared somehow... Anyone????
As a rule negative exponents are a blight if kept in the numerator. So always move the negative exponents from top to bottom and they become positive exponents in the denominator. Your response is 6 years old so your probably done with college.
it doesn't simplify you said it doesn't because b^2_4ac is negative which means the roots will be complex but can it still simplify even if the roots are complex
your 35 minute video on 25 differetiation examples is no longer available in Ireland or so youtube tells me. can you fix this please Patrick , thanks man
Why simplifying is needed when the total marks for a question is only 1 or 2? Just derivate the thing and be done with it. It may be needed in real life but not in exams.
