Using the Limit Definition of the derivative, find...

Transcript

00:01 Number one, where you're asked to do the limit as h approaches 0 of 2 to the h minus 1 over h using the limit definition.

00:10 What i'm thinking about is if i had a function that was named 2 to the x, and i'm trying to find this problem, then x is going to be 0, because f of 0 would equal 2 to the 0 power, which is equal to 1, see how that number is represented right here and you have minus zero.

00:35 So this is really the definition of the derivative for this function at, well, how about this? i'll just write it as f prime of zero.

00:47 So what's the derivative of 2 to the x? it is the natural log of 2 times 2 to the x.

00:56 And so if we did f prime of 0, it's equal to the x.

01:00 The natural log of 2 times 2 to the 0 power, which again, 2 to the 0 power equals 1.

01:06 So natural log of 2 times 1 is a natural log of 2.

01:11 So there's number 1.

01:13 I hope that made sense.

01:14 Looking at number 2, if we're just find, let me just name this g of x, just so i name it something new than f of x.

01:23 And we have 3x cubed.

01:26 I'm assuming you've learned the power rule, where what you do is you multiply the exponent, by the coefficient, and then you subtract one from your exponent, and that's your derivative.

01:41 If you haven't learned that yet, then i kind of ruined the fun.

01:45 But this answer's derivative would then be, oh, wait, i just realized.

01:51 So let me just put a giant x through all of that...

Question

Using the Limit Definition of the derivative, find $f'(x)$. $f(x) = 3x^2 + 7x - 2$

Question

Using the Limit Definition of the derivative, find $f'(x)$. $f(x) = 3x^2 + 7x - 2$

Please give Ace some feedback