Exponential functions differentiation intro | Advanced derivatives | AP Calculus AB | Khan Academy

Sal finds the derivative of a_ (for any positive base a) using the derivative of e_ and the chain rule. He then differentiates 8_3_.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[kennymaccaferri]

This is so well explained. After days and days of trying to get my head around a derivative of a forgetting curve this Mister Khan makes me see.... (don't know about tomorrow however, I will (according tot he equation I am working on - I will forget) but I suppose I could always come back). Thanks for your work Mister Khan.

[johnspence]

5:24 if confused at this point, to prove this is true, take a ln of both side (you get ln a= ln e ^lna), the rule of logs and exponents lets you bring down lna and put it as multiplier in front of lne. Since lne=1, you're left with lna= ln a, which is true. Therefore a is indeed = e to the power of (lna).

[cariboux]

This almost stretches my math abilities to their limit 😉 but not quite. I'm glad that I basically get it, because that just about blew my mind.

[tanishkchaturvedi]

Thanks sir you are the best teacher 😊🙏

[AndrewJames]

sorry I am a little confused, if the derivative of ln(x) is 1/x then why is the derivative of lna just lna? Should it not be 1/a?

[johnnolen]

You can also prove this using logarithmic differentiation.
y = a^x.
ln y = x·ln a.
1/y·dy/dx = ln a.
dy/dx = y· ln a.
dy/dx = a^x ln a. ◼

[SanjaySingh-rvrw]

What functions make up the composite function: e^(ln(a)x) at [Time: 3:08]?

[sergey_zatsepin]

Well, I don't understand why (ln(a)*x)' = ln(a), . it's because of e^x'=e^x but just otherwise?

[learnsanskrit_sabd]

t^2* e^-t=0.2, solve for t, how can we solve this

[trollifjell]

shouldn't a be a be a positive number greater than zero to make this work? Since you're using ln(a)

[tsukasa]

Hi khanacademy, Your videos helped me so much but i have 1 question. Isn't khan academy a non profit organization. You might probably get money for having 2.6 million subs.