Question

f(x) = x3 (8x^2 + 3)
f ' (x) = ?

Answer 1

we can either product rule it or expand and conquer

Answer 2

e and q is prolly the simplest

Answer 3

well my homework says to use product rule

Answer 4

then id go with product rule :)

Answer 5

but idk how to use the product rule

Answer 6

8 x^5+3 x^3 = f(x)
40x^4+9x^2=f'(x)

Answer 7

\[D[fg]=f'g+fg' \]

Answer 8

r and l work for me, as i tend to want to refer to them as left and right; but they come out a bit backwards

\[D[rl]=r'l+rl' \]

Answer 9

so f ' g stands for basically 8*5 raised to n-1 exponent, and then same for the three?

Answer 10

close, but lets try this route.

f'(x) = [x^3]' (8x^2 + 3) + x^3 (8x^2 + 3)'

that might be more intuitive

Answer 11

x^3' = 3x^2

and 8x^2+3 ' = 16x

you agree?

Answer 12

masc expanded instead of product ruling

Answer 13

okay, so for the x^3 ' you're substituting x-h - x/ h into it? since its te derivitive

Answer 14

i could, but since you are taking about product rule I assume you are past the "first principles" and onto the "rules" themselves

Answer 15

the first principles stuff is to prove the rules; once proved we can just use the rules

Answer 16

okay, so its X^3 ' * 8x^2?

Answer 17

product rule = uv' + vu'
x3 (8x^2 + 3)
u=x3 u'=3x^2
v=8x^2+3 v'= 16x
f'(x) = (x3)(16x)+(8x^2+3)(3x^2)
simplify

Answer 18

compter froze :/

Answer 19

okay gotcha