Answer:
see explanation
Step-by-step explanation:
Using the chain rule
Given
y = f(g(x)), then
= f'(g(x)) × g'(x) ← chain rule
and the standard derivatives
(
x ) = 
, (lnx) = 
(a)
Given
y = 
= 
× (
= × 
× (1 + x)
= × 
× 1
= 
= 
(b)
Given
y = ln sinx
= 
× (sinx)
= × cosx
= 
= cotx
Linear means that the y values go up in a fixed increment, k.
In the first one, you see that 3+4=7, 7+4=11, and so on, so you can immediately tell that it's linear.
The second one goes 3+5=8, then 8+7=15, then 15+6=21, which aren't the same numbers.
The third increases and decreases, so it's not linear.
The fourth goes 3+6=9, then 9+18=27, which you can immediately tell is not linear.
Therefore, the only linear table would be the first one.
Answer:
the are parallel to eachother
