Derivatives of Exponential Functions

[andrescuenca]

going back to grad school for mechanical engineering, and reviewing these videos brings back memories.

[brendapham]

Thanks Patrick! Please never stop making these videos! They are always such a great help. Even though my teacher is great at teaching calculus, it really helps to watch these videos to reinforce her lessons as well as see more examples!

[daniellelouisedonadillo]

i have a project in differential calculus and this video right here saves my life, god bless u patrick

[YEUHNBD]

you are unreal !!! ive never took calculus im in grade 12 right now and started from your first video in calc 1 to this one and understand everything ! you are amazing

[Miokien]

Solid example, thanks for putting in complex problems like problem b.

[d.b.p.]

Pay $1000 for a Calc I class to learn how to go to YouTube to teach yourself Calc I. Gotta love the government-subsidized American university system.

[horyshetpolio]

Patrick is a freaking awesome teacher. You never cease to amaze me. Great.. 
But it's too late to pass my Differential calculus subject this sem. Anyways i m looking forward for my return to Difcal through your vids

[taekwondotime]

This rule always trips me and I think it has to do with the fact that we get caught up doing derivatives of "e" all the time in calculus, and because it's a special case of the exponential rule, I tend to forget the "ln(base)" part at the end.

[bhardwajankit]

You are truly the best Math teacher on the planet!!

[Mimi-ghfv]

Thank you Patrick! You are way easier and consumable than Khan Academy. I watched his vid and felt even more confused. I saw the first page of your video and immediately my confusion was resolved.

[ironrose]

Hey Patrick! I'm not sure if you still read the comments on these videos, but I have two things:
1. Thanks for taking the time and effort to help people like me be successful- you do a great job and we sincerely appreciate it!
2. This may be off in left field here, but isn't the 5cos(x)cos(5x)-sin(x)sin(5x) a trig identity of cosine? Could you rewrite it as 5cos(a+b) = 5cos(x)cos(5x)-sin(x)sin(5x), so it simplifies to 5cos(x+5x) or 5cos(6x)?

[choccy]

woaw good timing! I have a test on this stuff plus curve sketching and optimisation and absolute extrema tomorrow!

[bhardwajankit]

you r really th best math teacher on this planet

[Warlord]

awesome. Now i'm ahead of my classmates. My teacher hasn't gotten to this point yet. My AP physics teacher taught it but rarely use more than the basic polynomials functions

[rureta]

Thank you much
I follow you from lraq

[JusenZurela]

Thanks for the tutorial, it really helps me.

[erinw.]

thank you so much. simple explanation with good examples

[chrismartin]

Trying to find the inflection point of an equation of curve. y=5.075e^(.2136x). equation goes from positive to negative. I have a lot of these to do so would like an online calculator. Can you point me in right direction. Did I give you enough information ?

[mindlessambience]

What if you were to differentiate the function   (1 + (1/x))^x for example?  Where the exponential base is not a constant...I am trying to prove that the derivative of this with respect to x is always positive for all x > 0.

[MONSTRO]

great tutorial thank you for your help Patrick! i was just wondering why in the last problem you didn't write ln of 2e at the end of the solution. I understand that ln of e (like you mentioned in the first rule) would simply give you 1, but in this case won't it actually give you a different value if it's ln of 2e (1.69), thus we'd have to write it into the last part of the solution? or do we just ignore ln of e even though there was a value in front of it?