Question

How do I find the derivative of f(x)=5x+9 at x=2?

Answer 1

the derivative is the same no matter what the point, and the derivative is the slope of the line, so maybe it meant "find the slope of the line at x=2"

Answer 2

Really? We're studying the derivatives with limits so I thought it would have something to do with that.

Answer 3

The derivative of a constant is alway zero, you can use the an^(a-1) rule to find that the derivative of that line everywhere is 5.

Answer 4

so the derivative of the eqn 5x + 9 is just 5
so the slope of the line at any point is 5
so at x=2, slope = 5

Answer 5

Oh, great! Thank you

Answer 6

ooo, shiny, thanks!

Answer 7

you get how to find the derivative of an eqn tho...?
that;s the important bit

Answer 8

Yes! Just the slope, right?

Answer 9

yeah... but what about if f(x) = 2x^2 +10x
so whats the slope at x=2...?

Answer 10

That's actually similar to the next question on my assignment! Haha but that's a good question.. Is there a certain formula I can use like mitodoteira said?

Answer 11

yeah, for the derivative, what i do is:
\[f(x) = 2x ^{2} + 10x\]

so derivative is:
\[f'(x) = 2\times(2x ^{(2-1)}) + 1\times(10^{1-1})\]

Answer 12

Why did you use those exponents?

Answer 13

so take whatever x is to the power of... and times it in front

then minus one from that power

see how the 2 comes down and you multiply it by the other 2
and the x^2 becomes x^1

then the 1 comes down and you multiply it by the 10
and the x^1 becomes x^0... which equals 1
so it just becomes :

f'(x) = 4x + 10

Answer 14

chose those powers just randomly

Answer 15

so at x= 2, slope = 4x +10 = 4*2 + 10 = 18

Answer 16

now you try on
f(x) = 3x^6 +10x^4

Answer 17

So for \[-12x^2+9x\] at x=6, it would be (i'm having difficulty figuring out the equation option) 2*(12x^(2-1))+1*9^(1-1) ?

Answer 18

I just decided to use the equation that I'm trying to figure out-sorry!

Answer 19

yep that's it
so -24x plus 9 is the slope

then sub in x=6

Answer 20

Then, it would be 144x+9?

Answer 21

Oh, I thought I was supposed to square it.

Answer 22

wait... what?

Answer 23

no, the exponent is timeed by the number in front

Answer 24

Okay! I understand now. So then it would be (-24*6)+9=-135

Answer 25

so if it's x^a
derivative is ax^(a-1)

so
2*(12x^(2-1))+1*9^(1-1)

Answer 26

That makes sense now.

Answer 27

yep, u got it
just quickly try the derivative of this:
f(x) = 3x^6 +10x^4

Answer 28

6(3x^(6-5)+1(9^(4-4))
Is this right so far?

Answer 29

18x+9, so the derivative would be 18 if it's not at a certain place?

Answer 30

not quite...
f(x) = 3x^6 +10x^4
so
f'(x) = 6*3 x^(6-1) + 4*10 x^(4-1)

Answer 31

so 18x^5 +40x^3

Answer 32

I thought I had to make them both even out to 1 and zero, but I see that now. So no matter what the exponents are, I always subtract 1 from them in that equation?

Answer 33

yep there u go

Answer 34

Thank you so much! Is there anything special I have to do for fractions? For example, \[f(x)=-11/9\] at 9? Also, if there are no powers, or possibly fractions involved, the derivative is just the slope?

Answer 35

there's no x in that eqn...?

Answer 36

-11/9x

Answer 37

like:
\[\frac{ -11 }{ 9x } or (\frac{ -11 }{ 9 })x\]

Answer 38

Sorry, I misread it. It was (-11/x) at x=9

Answer 39

ah, ok
so 1/ anything is the same as anything to the power of -1
eg
\[\frac{ 1 }{ 5 } = 5^{-1}\]

Answer 40

so
\[\frac{ 11 }{ x } = 11 x ^{-1}\]

Answer 41

Yes.. would that make the derivative 11, or do we still have to work with the exponent?

Answer 42

still need to work with the exponent
so (-1 - 1) = ???

Answer 43

-2

Answer 44

so it becomes (-1) * (-11) *(x^-2)

Answer 45

follow ok...?

Answer 46

more explainin...?

Answer 47

Yeah, I'm just not sure what to do after that other than solve, and in decimal form, I got -0.00826, but I feel like that is incorrect.

Answer 48

9^2 = 81
so 11/81 = 0.1358

Answer 49

Wow, that was a silly mistake of mine. I got it now! Thank you so much

Answer 50

always welcomes