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Math Help - Having trouble with derivative..please help.

  1. #1
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    Having trouble with derivative..please help.

    Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.


    h'(x) =

    I got -arctan x dx/x^2..think it's wrong
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  2. #2
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    Quote Originally Posted by Jgirl689 View Post
    Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.


    h'(x) =

    I got -arctan x dx/x^2..think it's wrong
    If h(x)=\int_a^{g(x)} f(t) dt, then:

    h'(x)=f\left(g(x)\right) g'(x).

    In your answer, It should be arctan \left( \frac{1}{x} \right) not just arctan(x).
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  3. #3
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    Quote Originally Posted by Jgirl689 View Post
    Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.


    h'(x) =

    I got -arctan x dx/x^2..think it's wrong
    if h(x) = \int_a^u f(t) \, dt , then h'(x) = f(u) \cdot \frac{du}{dx}

    h'(x) = \arctan\left(\frac{1}{x}\right) \cdot \left(-\frac{1}{x^2}\right)
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  4. #4
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    Let \arctan t = F'(t)

    Then h(x) = \int _6 ^{1/x} \arctan t dt = F(1/x) - F(6)

    h'(x) = F'\left(\frac{1}{x}\right) \cdot \left(-\frac{1}{x^2}\right)
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