AP Calculus 1.3 Derivatives

AP Calculus 1.3 Derivatives. Compute the limit.

AP CalculusDerivatives
LanguageEnglish Language
MPAC 1Reasoning with definitions and theorems
MPAC 3Implementing algebraic/computational processes

Transcript

00:22

all right If we were to rush headlong into this

00:24

problem we bash our heads into a brick wall instead

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we should try and simplify it First recall that the

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formal definition of a derivative is equal to the limit

00:34

as x approaches Si of f of x minus f

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of c all over the quantity x minus c look

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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

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

00:54

sorted out we just have to take the derivative of

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the to the co sign of a to find the

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answer Remember that the derivative of k to the power

01:01

of axe is equal to k to the power of

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axe times the natural laws of k using that formula

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For this case we get e to the power of

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co sign a times the natural log of e since

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

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

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in either the power of co sign a which is

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coast on a we need to find the derivative of

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it which is negative sign of a We multiply that

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to what we currently have Conduce um quick simplification and

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

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

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negative sign of a Our answer matches up with the

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