Thread: Differentiation and trigonometric integrals

Good afternoon everybody! I recently started taking calculus 2 at university and the class picks up like we never missed a day between calc 1 and calc 2. We jumped right in and I'm rather rusty. I use khan academy often but was hoping somebody could help me review/teach me with differentiation and trig integrals.

Anyways, here are my problems that I'm working on. Yes, they're rather simple but I've not done calculus in 4 or so months:

Differentiate:
1. y= 4x^3 -2x

Spoiler for Answer:

12x^2 -2

2. y= sqrt(2x-4)

Spoiler for Answer:

(2x+4)^-.5

3. y= x^3 tan(x)

Spoiler for Answer:

(3x^2)(tan x)+(x^3)(sec^2 x)

4. y= sin(x^2)

Spoiler for Answer:

2x cos(x^2)

5. y= (x+4)/(x-2)

Spoiler for Answer:

(x+4)((-x+2)^2)+(x-2)^-1

Integrate:
6. ∫ (cos x- sin x)dx

Spoiler for Answer:

sin x+ cos x+ C

7. ∫ sqrt(x)dx (Definite- solved at 4 and 1)

Spoiler for Answer:

2x^1.5 (Waiting to calculate this one )

8. ∫ cos(x^2)xdx

Spoiler for Answer:

1-sin^2 x + C

9. ∫ (sin^2 x cos x)dx

Spoiler for Answer:

sin^3 x/3 + C

10. ∫ (tan x sec^2 x)dx

Spoiler for Answer:

sec^2 x + C

Those are the questions I'm currently working on. I'd just like somebody to discuss something related with me or check my work. Thanks in advance!