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Math Help - Calculus I level question, find the derivative?

  1. #1
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    Calculus I level question, find the derivative?

    Given: r(2)=4, s(2)=1, r'(2)=-1, s'(2)=3, s'(4)=3, find the derivatives or state what information you would need to find them for:
    H'(2) if H(x)=r(x)s(x)
    H'(2) if H(x)=square root of r(x)
    H'(2) if H(x)=r(s(x))
    H'(2) if H(x)=s(r(x))

    Answers to any would be appriciated, please show your work
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  2. #2
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    1).H(x) = r(x)s(x)

    differentiate, using product rule,

    H'(x) = r(x)s'(x) + r'(x)s(x)

    H'(2) = r(2)s'(2) + r'(2)s(2)

    H'(2) =(4)(3) + (-1)(1) = 11


    2).

    H(x) = \sqrt{r(x)}

    differentiate,

    H'(x) = \frac{1}{2\sqrt{r(x)}}r'(x)

    H'(2) = \frac{1}{2\sqrt{r(2)}}r'(2)

    H'(2) = \frac{1}{2\sqrt{4}}(-1)

    H'(2) = \frac{-1}{4}

    3).

    H(x) = r(s(x))

    differentiate, using chain rule,

    H'(x) = r'(s(x)).s'(x)

    H'(2) = r'(s(2)).s'(2)

    H'(2) = r'(1).(3)

    H'(2) = 3 . r'(1)

    we need the value of r'(1) to find H'(2).

    4) You try this part. Did you get it ???
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