Question

Let y = (6 - 2 x)^4.
Find the first and second derivatives of y.

dy/dx= A ( 6 - 2x )B

d2y /dx2 = C ( 6 - 2x )D

Answer 1

A=4
B=-2
C=-24
D=-2

Answer 2

i put that in for a= 4 and said it was wrong

Answer 3

y'= 4(6-2x)^3 (-2)
y'= -8(6-2x)^3

y''= -24(6-2x)^2 (-2)
y''=48(6-2x)^2

Answer 4

ok thanks

Answer 5

use chain rule
(6 - 2 x)^4

g(x) = x^4
g'(x) = 4x^(3)
f(x) = 6-2x
f'(x) = -2

y' = (4(6-2x)^(3)) (-2)
=-8(6-2x)^(3)
use chain rule again

g(x) = -8x^3
g'(x) = -8(3)x^(2)
f(x) = 6-2x
f'(x) = -2

y'' = (-8(3)(6-2x)^(2))(-2)
y'' = 48(6-2x)^(2)

Answer 6

ok

Answer 7

Derivatives are really easy to understand especially chain rule if you split them up like I have

Answer 8

A = 4, B = -2, C = -24, D = -2

y = (6 - 2 x)^4.
y' = 4 ((6 - 2 x)^3 ( -2)
= -8 ((6 - 2 x)^3
y" = - 24 (6 - 2 x)^2 ( -2)
= 48 (6 - 2 x)

Answer 9

I means = 48 (6 - 2 x)^2