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Math Help - Questions regarding Trig. Derivatives

  1. #1
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    Questions regarding Trig. Derivatives

    Hello, I am trying to find the second derivative of 7 secx, and If I did it correctly, I got 7(sec^3x+secxtan^2x)

    I also have another question, I think I need to do the product rule, but I have to find the first derivative of 9x^2 sinx + 18 cosx -18 sinx Im not sure how to go about using the product rule with this, as there is like 3 terms. Any help would be appreciated, Thanks!
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  2. #2
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    your 2nd derivative for 7\sec{x} is correct.

    for the second problem, use the product rule for the first term only ... take the derivative of the last two terms as usual.
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  3. #3
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    Ok, thanks!

    hmmm, so the first derivative of ,

    would be: 9x^2cosx+18xsinx+18sinx-cosx ?
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  4. #4
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    not quite, note the last two terms ...

    \frac{d}{dx}(9x^2\sin{x} + 18\cos{x} - 18\sin{x}) =

    9x^2\cos{x} + 18x\sin{x} - 18\sin{x} - 18\cos{x}
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  5. #5
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    haha, wow, thats what I had written on my paper, but I typed it wrong.

    edit: wait, doesnt the 18 in the last term go to 0, thats where I wrote -cosx, cause you took teh deriv, of the middle term, but when u take the deriv of the last term -18sinx should it go to -cosx, since deriv of -18 is 0
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  6. #6
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    remember the constant multiple rule?

    \frac{d}{dx} [k \cdot f(x)] = k \cdot f'(x)

    so ...

    \frac{d}{dx} [-18\sin{x}] = -18 \cdot \cos{x}
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  7. #7
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    ohh, yeah I forget about that rule, doenst seem to be used much - maybe cause I miss it when doing a problem?
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