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Math Help - Chain rule for trig function

  1. #1
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    Chain rule for trig function

    Find the second derivative:

    <br />
f(x) = \frac{1}{x} + \tan(x)<br />
    <br />
f'(x) = -x^{-2} + \sec^2(x)<br />
    <br />
f"(x) = 2x^{-3} + 2\sec(x)\sec(x)\tan(x)<br />
    <br />
f"(x) = \frac{2}{x^3} + 2\sec^2(x)\tan(x)<br />


    My teacher got f"(x) = \frac{2}{x^3} + 2\sec^2(x)\tan^2(x) but I think she just put the tanx in for u on accident... Is my second derivative correct?
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by tom ato View Post
    Find the second derivative:

    <br />
f(x) = \frac{1}{x} + \tan(x)<br />
    <br />
f'(x) = -x^{-2} + \sec^2(x)<br />
    <br />
f"(x) = 2x^{-3} + 2\sec(x)\sec(x)\tan(x)<br />
    <br />
f"(x) = \frac{2}{x^3} + 2\sec^2(x)\tan(x)<br />


    My teacher got f"(x) = \frac{2}{x^3} + 2\sec^2(x)\tan^2(x) but I think she just put the tanx in for u on accident... Is my second derivative correct?
    I think you are correct.
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