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Math Help - Help Desperately Needed (chain rule)

  1. #1
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    Help Desperately Needed (chain rule)

    Working with the chain rule. Have two sets of problems, and I have no idea how to even get started. VERY confused/frustrated. Here are my two problem sets:

    Code:
    Suppose k '(1) = 4. 
    
    (a) If f(x) = k(7x), find f '(1/7).
    f '(1/7)=
    
    (b) If g(x) = k(x+ 6), find g '(-5).
    g '(-5) =
    
    (c) If h(x) = k(x / 11), find h '(11).
    h '(11) =
    and

    Code:
    Suppose f(2) = 4 and f '(2) = 7. Find the derivatives 
    of the following functions. 
    
    (a) g(x) = sqrt(f(x)) 
    g '(2)= 
    
    (b) h(x) = 1/f(x) 
    h '(2)=
    If anyone can help me out it would be greatly appreciated. I have to turn this in by 11pm.
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  2. #2
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    Quote Originally Posted by keyweez360 View Post
    Working with the chain rule. Have two sets of problems, and I have no idea how to even get started. VERY confused/frustrated. Here are my two problem sets:

    Code:
    Suppose k '(1) = 4. 
    
    (a) If f(x) = k(7x), find f '(1/7).
    f '(1/7)=
    
    (b) If g(x) = k(x+ 6), find g '(-5).
    g '(-5) =
    
    (c) If h(x) = k(x / 11), find h '(11).
    h '(11) =
    and

    Code:
    Suppose f(2) = 4 and f '(2) = 7. Find the derivatives 
    of the following functions. 
    
    (a) g(x) = sqrt(f(x)) 
    g '(2)= 
    
    (b) h(x) = 1/f(x) 
    h '(2)=
    If anyone can help me out it would be greatly appreciated. I have to turn this in by 11pm.
    Chain rule: if f(x) = g(h(x)) then f^{'}(x) = g^{'}(h(x)) \, h^{'}(x).

    I'll do Q1 (a):

    f^{'}(x) = k^{'}(7x) \, (7x){'} = 7 k^{'}(7x).

    Therefore f^{'}(1/7) = 7 k^{'}(7 (1/7)) =  7 k^{'}(1) = (7) (4) = 28.


    As for Q2:

    Again using the chain rule:

    (a) g^{'}(x) = \frac{1}{2} \frac{1}{\sqrt{f(x)}} \, f^{'}(x).

    (b) h^{'}(x) = - \frac{1}{[f(x)]^2} \, f^{'}(x).
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  3. #3
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    Fantastic!
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