The math help thread

1. g'(t)=e^(1+3t)^2*2(1+3t)*3
2. y'=e^-t^2+te^-t^2*2(-t)*-1




Also I got a probability question:
There's a 100% chance i get <60% for psych.
There's a 36% chance i get <50% for psych.
There's a 35% chance i get <60% for calc.
There's a 3% chance i get <50% for calc.
There's a 60% chance i get <60% for physics.
There's a 20% chance i get <50% for physics.

I will get kicked out of uni if I fail 2 course (get <50%). or if I fail 1 course and get <60% on 2 other courses.
What's my chance of getting kicked out.

For each of the three classes you have three disjoint possibilities: more than 60% (call this 'A'), between 50 and 60% (B), and below 50% ©. Also, for the final result you have two possibilities: pass (P) and fail (F).
F = 2 C and 1 anything, or 1 C and 2 B
P = 3 B or higher, or 1 C, 1 A, 1 B or higher

So, making a tree:
0% psych-A
64% psych-B
-> 65% calc-A (P)
-> 32% calc-B
--> 40% physics-A (P)
--> 40% physics-B (P)
--> 20% physics-C (F)
-> 3% calc-C
--> 40% physics-A (P)
--> 40% physics-B (F)
--> 20% physics-C (F)
36% psych-C
-> 65% calc-A
--> 40% physics-A (P)
--> 40% physics-B (P)
--> 20% physics-C (F)
-> 32% calc-B
--> 40% physics-A (P)
--> 40% physics-B (F)
--> 20% physics-C (F)
-> 3% calc-C (F)

Summing up all the F's...
0.64 * 0.32 * 0.2
0.64 * 0.03 * 0.6
0.36 * 0.65 * 0.2
0.36 * 0.32 * 0.6
0.36 * 0.3
= 0.2764 = 27.64% chance.