Question

Table of derivatives. I'm not sure how to do this.

Answer 1

@karatechopper @Shane_B

Answer 2

do you know how to find the derivative of two functions multiplied together?

d (u v) = u dv + v du is the short-hand way of writing the rule.

Answer 3

ohh....so I can apply the product rule to this?

Answer 4

@phi
Could you check my work?

Answer 5

yes, what did you get ?

Answer 6

d/dx (f(-2)*g(-2))
[d/dx (f(-2)]*g(-2) + [d/dx g(-2)]*f(-2)
-2*4 + 3*3
-8 +9 = 1

Answer 7

yes, that is correct. but I would use x until the very end, when you plug in -2 for x
f(-2) is just 1 point and there is no derivative. so write it like this

d/dx (f(x) * g(x)) = df(x)/dx * g(x) + dg(x)/dx * f(x)
now replace x with -2, and get your answer.

Answer 8

Did I do the equation in the wrong way?

Answer 9

you did it correctly, but you show taking the derivative of f(-2) (for example)
you can only take the derivative of f(x)

so it looks better to take the derivative of f(x) and g(x), then after you get the formula, replace x with -2.

Answer 10

So....
[d/dx (f(x)]*g(x) + [d/dx g(x)]*f(x)
[(f'(-2)]*g(-2) + [g'(-2)]*f(-2)
-2*4 + 3*3

Answer 11

yes, that looks good.