AP Calculus 1.3 Derivatives. Compute the limit.

AP Calculus | Derivatives |

Language | English Language |

MPAC 1 | Reasoning with definitions and theorems |

MPAC 3 | Implementing algebraic/computational processes |

all right If we were to rush headlong into this

problem we bash our heads into a brick wall instead

we should try and simplify it First recall that the

formal definition of a derivative is equal to the limit

as x approaches Si of f of x minus f

of c all over the quantity x minus c look

similar to this problem Yeah fx And this problem is

just even the coastline x This problem is merely a

fancy way of asking for the derivative of the to

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

sorted out we just have to take the derivative of

the to the co sign of a to find the

answer Remember that the derivative of k to the power

of axe is equal to k to the power of

axe times the natural laws of k using that formula

For this case we get e to the power of

co sign a times the natural log of e since

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

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

in either the power of co sign a which is

coast on a we need to find the derivative of

it which is negative sign of a We multiply that

to what we currently have Conduce um quick simplification and

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

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

negative sign of a Our answer matches up with the

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