Question

find derivative
g(x)= 6-8x^2, a=2

Answer 1

Is the a-2 relevant?

\[g(x) = 6-8x^2\]
the derivative of say\[x^n \rightarrow nx^{n-1}\]
So \(x^2 \rightarrow 2x\). does that make sense?

Answer 2

oops! it's suppose to be a=2.

Answer 3

Ah ok, well let's start by finding the derivative anyway. what does 8x^2 become?

Answer 4

Oh yeah that was easy.

Answer 5

-16 x

Answer 6

so the final derivative is?

Answer 7

(remember that a number is simply nx^1

Answer 8

the answer is -16(2) = -32

Answer 9

I had trouble with this one g(x) = 6x ^2 e^-x

Answer 10

is that\[g(x) = 6x^2 e^{-x}\]?

Answer 11

yes

Answer 12

Ok use, the chain rule. Do the differential of one bit times the other + the difference of the other times the first. Does that make sense?

Answer 13

Yeah, I have (12x)(e^-x)+(-e^-x)(6x^2)

Answer 14

Good job

Answer 15

but then I don't know how the answer turns to 6xe^-x (2-x)

Answer 16

You can multiply that out and then treat the different parts as separate differentials.
\[6xe^{-x}(2-x)=12xe^{-x}-6xe^{-x}\]and then differentiate them separately

Answer 17

Ah I see. Thanks!!!