Question

PLEASE HELP WILL GIVE MEDAL
The position of an object at time t is given by s(t) = -2 - 6t. Find the instantaneous velocity at t = 2 by finding the derivative.

Answer 1

replace t by 2 and then solve

Answer 2

-14?

Answer 3

yes

Answer 4

that's it?

Answer 5

hmm i guess find derivative

Answer 6

i guess nope*

Answer 7

instantaneous velocity at x=a is f'(a).

Answer 8

yes, you need the derivative. And then to plug in 2 for t.

Answer 9

how do i get the derivative?

Answer 10

differentiate (find derivative of) of each term.

What is the derivative of -6x?
What is the derivative of -2?

Answer 11

idk how to find it

Answer 12

do you know the power rule?

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (x^n)=n\cdot x^{n-1} }\)

Answer 13

(d/dx is a notation for a derivative)

Answer 14

Have seen this rule before?

Answer 15

I will give you an example:

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (x^3)=3\cdot x^{3-1} =3x ^2 }\)

Answer 16

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (x^1)=? }\)

Answer 17

1*x^0 =1

Answer 18

yes.

Answer 19

okay so how do i use that for the question?

Answer 20

Now, there is a different rule, with a constant C.

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (c~x^n)=c \cdot \left( \frac{d}{dx}x^n \right)=c\cdot \left( n\cdot x^{n-1} \right) }\)

Answer 21

you are basically taking the constant out.

Answer 22

For example,

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (3~x^4)=3 \cdot \left( \frac{d}{dx}x^4 \right)=3\cdot \left(4\cdot x^{4-1} \right) = 3\cdot \left(4 x^{3} \right)=12x^3 }\)

Answer 23

You need,

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (-6~x^1)= }\)

Answer 24

(I took out a 3, and YOU are taking -6 out)

Answer 25

i am still confused about how i take the -6 out

Answer 26

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (-6~x^1)=(-6) \cdot \left( \frac{d}{dx}x^1 \right)=~~....}\)

Answer 27

see?

Answer 28

lost?

Answer 29

yep

Answer 30

\(\color{slate}{ \displaystyle \frac{d}{dx} (c~x^n)=c \cdot \left( \frac{d}{dx}x^n \right)=c\cdot \left(n\cdot x^{n-1} \right) = c\cdot \left(n x^{n-1} \right)=cnx^{n-1} }\)

Answer 31

Example,

\(\large\color{slate}{ \displaystyle \frac{d}{dx} (-2~x^6)=(-2) \cdot \left( \frac{d}{dx}x^6 \right)=(-2)\cdot \left(6\cdot x^{6-1} \right) = (-2)\cdot \left(6 x^{5} \right) \\ ~\\~\\=-18x^{5} }\)

Answer 32

do you see what I am doing in the example?

Answer 33

(I am separating the -2, and the derivative of x^6)

Answer 34

\(\large\color{black}{ \displaystyle \frac{d}{dx}\left( -6x^{^{_{\Large 1}}} \right)=(-6)\frac{d}{dx}\left( x^{^{_{\Large 1}}} \right) }\)