We are given that y = t^2 , t = 3p+5 and p = 6x^2 . What is dy/dx?

y =t^2 .

t
=3p+5

p = 6x^2

are the give
relations. To find dy/dx.

y  =
t^2.

y  = (3p+5)^2 , as t =
3p+5

y = {3(6x^2)+5}^2 =
(18x^2+5)^2

y' = 2(18x^2+5)^(2-1)
*(18x^2+5)'

y' =
2(18x^2+5)(18*2x)

y' =
72(18x^2+5)x.

Alternative
method:

Therefore , y = (18x^2+5)^2 =
2

To solve this we try to find y  in terms of p and x
interms p and then find dy/dp  and dx/dp. Then we use
:

dy/dx = (dy/dp)/(dx/dp).

y =
t^2 and t = 3p+5. We eliminate t and find y in terms of
p.

y= (3p+5)^2.

We
differentiate  y wrt p:

y'
={(3p+5)^2}'

y' =
2(3p+5)^(2-1)*(3p+5)'

y'
=2(3p+5)*3

y' =
6(3p+5)............(1).

6x^2 =
p

We differentiate both sides of the equation  wrt p 
:

6*2x dx/dp = 1

dx/dp =
1/12x............(2).

Therefore using(1)
and(2):

dy/dx = (dy/dp)/(dx/dp) =  6(3p+5)/(1/12x) =
12*6(3p+5)

Therefore

dy/dx =
72(3p+5)x

dy/dx = 72(18x^2+5)x as, p =
6x^2.