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Math Help - Trigonometric and Natural Log Derivatives

  1. #1
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    Exclamation 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.
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Okay, first of all: Do you know what the product rule, power rule, chain rule are?
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  3. #3
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    Yes, taking the time use them is another story.
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  4. #4
    Math Engineering Student
    Krizalid's Avatar
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    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.

    --

    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.

    --

    To check your work, this will be helpful.
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