# Thread: Trigonometric and Natural Log Derivatives

1. ## Trigonometric and Natural Log Derivatives

Hey all, I've got a rather large assignment due tomorrow and I was wondering if I could get some help with derivatives.

1. y = 2sinxcosx

2. s = cot(2/t)

3. r = sec(1 + 3δ)

4. y = 5 + 2x - 7x^2 - 4x^3

5. y = ln(x^1/2)

6. y = e^(1 + ln + x)

7. y = x/[(2x + 1)^1/2]

8. y = x^3 (2x^2 + 3x - 5)^4

9. y = sin^2 (3x - 2)

10. y = cos(tanx)

11. y = csc^-1 (x^2 + 1)

12. y = sin^-1 (1 - x)

I grasp the basic concept and rules necessary, it's just applying them that I have trouble with. It would be great if I could get some examples to reference when I'm studying for the chapter test.

Thanks.

2. Okay, first of all: Do you know what the product rule, power rule, chain rule are?

3. Yes, taking the time use them is another story.

4. Okay.

For the first one, you can take its derivative but before doing that apply the make-up:

$y=2\sin x\cos x=\sin2x.$

Now from there is easy to take the derivative, you only need the chain rule.

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Also $(e^u)'=e^u\cdot u'$ & $(\ln u)'=\frac1u\cdot u'.$

And $(\arcsin u)'=\frac1{\sqrt{1-u^2}}\cdot u'.$

I don't remember the formula for $(\text{arccsc}\,u)',$ but you can derive it easily.

Tell us what you've got.

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