Chain Rule with the Quotient Rule Problem 3 (Calculus 1)

This is a really good problem on finding the derivative using the Quotient Rule and the Chain Rule. Applying the Chain Rule, to find the derivative of the function in the denominator, isn't too bad. However, we're left with a mess! We express everything without negative exponents so that way we can easily simplify this complex fraction. After a little work we get a nice, simplified answer for the derivative. This problem or one like it is usually a standard test/exam question in calculus 1.
Shortcuts for the Chain Rule - General Power Rule and General Exponential Rule: • Shortcuts for the Chai...
Chain Rule with the Quotient Rule Problem 1: • Chain Rule with the Qu...
Chain Rule with the Quotient Rule Problem 2: • Chain Rule with the Qu...
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[@erinphillips5431]

This is the best video I’ve seen on this topic. Thank you for explaining clearly.

[@alphakr8894]

Amazing Video! Very clear, I've been stressing about my exam and this made things very clear! You deserve much more subscribers than you have.

[@BlackTshirtMathProfessor]

Thanks! Good luck on your exam 💪🏻

[@valeriagranados5932]

Very understandable thank you so much teacher!!

[@JRyanEE]

Thank you, this is was easier to understand compared to the other examples I was trying to learn from.

[@louieavila3987]

THANK YOU SO MUCH!!!! TEACHER DIDNT EXPLAIN THIS AND MATHWAY WAS NO HELP EITHER!

[@user-no3gn5mu2v]

Thanks a lot for explaining it so clearly and finding such an encompassing example! hopefully more people will discover your channel ! :)

[@taehyungtwin]

tysm i was about to kms over this

[@amogelangntsoane5900]

bout to watch, if it doesnt help me, im doin it.

[@deeznuts8624]

Thank you sir , your videos on caculus are amazing , i am understanding the concepts a lot better . Dont get demotivated by views .

[@BlackTshirtMathProfessor]

Thanks! It is a bit discouraging to put so much time into a video to only have single digit views but it will grow with time. Thanks for the motivation!

[@SalamaAMV]

thank u very much sir i learned a lot

[@BlackTshirtMathProfessor]

I’m glad that it helped

[@ronaldosburner7]

appreciate ur work, keep it up!.

[@NASALunarLight]

Would it be embarrassing to say that I was attempting to use f(x+h)-f(x)/h as a reference to solve this problem? When it was just quotient rule all along? Oops.

[@sarahyy.yy_3]

Same😭

[@juliannafotheringham7101]

AMAZING THANK YOU

[@nkosikhonabengu641]

if I could I would like this video 10 000 times🙌👍

[@johnmartin3275]

I want you as my teacher lol

[@fatema7589]

Thank uuuu❤

[@lourdesnevarez1586]

How did you start off by leaving the denominator as (x^2+1) when it was (x^2+1)^2? how did you get rid of the square? at point 6:48 ? thank you!

[@excdragaming1785]

raising to power of 2 cancels the square root

[@isajones9146]

Im confused how you got the minus x^2 in the numerator

[@BlackTshirtMathProfessor]

It comes from x * x/sqrt(x^2 + 1) after multiplying the numerator and denominator by sqrt(x^2 + 1). Think of the first factor of x as x/1 and then multiply and cancel common factors.

[@sokohannette3702]

I don't understand how you got 2x

[@rapmayuga7620]

Derivative of x²+1 is 2x because u cancel the constant +1 and you bring down the squared exponent then -1 the exponent

[@thatomofolo452]

Awesomeness

[@VictoriaNondo]

I don't understand how you got 2x

[@tcggggg]

2x was the derivative of the inner part of the parenthesis.