ShmoopTube

00:00

Thank you We sneak and here's your shmoop to shore

00:05

Brought to you by brick walls wherever you find one

00:09

There's probably a stand up comedian nearby All right compute

00:13

the limit of this ugly beast you see right here

00:16

All right And here the potential answers thinking thinking uh

00:22

all right If we were to rush headlong into this

00:24

problem we bash our heads into a brick wall instead

00:27

we should try and simplify it First recall that the

00:30

formal definition of a derivative is equal to the limit

00:34

as x approaches Si of f of x minus f

00:38

of c all over the quantity x minus c look

00:42

similar to this problem Yeah fx And this problem is

00:45

just even the coastline x This problem is merely a

00:48

fancy way of asking for the derivative of the to

00:51

the coastline of access acts approaches a now that that's

00:54

sorted out we just have to take the derivative of

00:56

the to the co sign of a to find the

00:58

answer Remember that the derivative of k to the power

01:01

of axe is equal to k to the power of

01:03

axe times the natural laws of k using that formula

01:07

For this case we get e to the power of

01:09

co sign a times the natural log of e since

01:13

we're studious test takers we won't forget the chain rule

01:16

number That one general means that since there's another function

01:19

in either the power of co sign a which is

01:22

coast on a we need to find the derivative of

01:24

it which is negative sign of a We multiply that

01:28

to what we currently have Conduce um quick simplification and

01:31

get rid of the limited re since that's just one

01:35

and we're left with either the coastline of a times

01:38

negative sign of a Our answer matches up with the

01:41

answer choice eh Hey that was not significantly less painful 00:01:45.04 --> [endTime] than taking a brick wall Approach your forehead

Full Transcript