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Math Help - Derivative of another function's derivative?

  1. #1
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    [Solved] Derivative of another function's derivative?

    So we just started getting into derivatives in class, and I understand the concept and the formulas. I've read through my textbook several times and can't come across a similar problem. I'm sure I'm just overlooking something I know. But the more I stare at this question the angrier I get because it seems so simple. Also, if you could tell me what this 'type' of problem is, I'd appreciate it.

    Consider the function h(x), for which h(5) = 2 and h'(5) = 4.
    Let f(x) = h(x) / x. Then f'(5) = ?

    Thanks in advance.
    Last edited by jjtjp; February 14th 2013 at 06:06 PM.
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Derivative of another function's derivative?

    (using the quotient rule)f'(x) = \frac{ h'(x)x - h(x)}{x^2} so f'(5) = \frac{ h'(5)5 - h(5)}{5^2} = \frac{4*5 - 2}{25} so f'(5) = \frac{18}{25}
    Thanks from jjtjp
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    Re: Derivative of another function's derivative?

    Thanks I was trying to set up something like that but I was having issues because the formula given in class for quotient functions was as follows:
    \frac{numderiv * denom - num * denom deriv}{denom^2} and I was getting hung up because the derivative of x wasn't defined. I forgot that it was always 1. Is that a correct understanding? Thanks again so much. You've made my night!
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    Re: Derivative of another function's derivative?

    Quote Originally Posted by jjtjp View Post
    Thanks I was trying to set up something like that but I was having issues because the formula given in class for quotient functions was as follows:
    \frac{numderiv * denom - num * denom deriv}{denom^2} and I was getting hung up because the derivative of x wasn't defined. I forgot that it was always 1. Is that a correct understanding? Thanks again so much. You've made my night!
    yes
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    Re: Derivative of another function's derivative?

    In fact, the "derivative" is a generalization of the "slope" of a straight line so the derivative of any linear function, ax+ b is just the constant slope, a. Here, a= 1 and b= 0.
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