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Math Help - second derivative

  1. #1
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    Post second derivative

    f(x) = (3x+1)^3

    f'(x) = 3(3x+1)^2(3)
    f'(x) = 9(3x+1)^2

    f"(x) = 9[(2)(3x+1)(3)] + [9(3x+1)^2]
    f"(x) = 54(3x+1) + 9(3x+1)^2
    f"(x) = 9(3x+1)[6 + (3x+1)^2]
    f"(x) = 9(3x+1)(7+3x)

    Am I correct?
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  2. #2
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    Quote Originally Posted by startingover View Post
    f(x) = (3x+1)^3

    f'(x) = 3(3x+1)^2(3)
    f'(x) = 9(3x+1)^2

    f"(x) = 9[(2)(3x+1)(3)] + [9(3x+1)^2]
    f"(x) = 54(3x+1) + 9(3x+1)^2
    f"(x) = 9(3x+1)[6 + (3x+1)^2]
    f"(x) = 9(3x+1)(7+3x)

    Am I correct?
    What's going on in line 4? All you need to do is:
    f''(x) = 9 * 2(3x + 1)*3 = 54(3x + 1) = 162x + 54

    -Dan
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  3. #3
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    Quote Originally Posted by startingover View Post
    f(x) = (3x+1)^3

    f'(x) = 3(3x+1)^2(3)
    f'(x) = 9(3x+1)^2

    f"(x) = 9[(2)(3x+1)(3)] + [9(3x+1)^2]
    f"(x) = 54(3x+1) + 9(3x+1)^2
    f"(x) = 9(3x+1)[6 + (3x+1)^2]
    f"(x) = 9(3x+1)(7+3x)

    Am I correct?
    You are right until you decided to take the second derivative:

    f(x) = (3x+1)^2
    f'(x) = 3(3x+1)^2*(3)

    Now in order to get f''(x) you must use the product rule (not the triple product rule as constants hold over) thus:

    f''(x) = (3)*(2(3x+1))*(3)*(3)

    You do not have to but I choose to simplify so

    f''(x)= 54(3x+1)
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by qbkr21 View Post
    You are right until you decided to take the second derivative:

    f(x) = (3x+1)^2
    f'(x) = 3(3x+1)^2*(3)

    Now in order to get f''(x) you must use the product rule (not the triple product rule as constants hold over) thus:

    f''(x) = (3)*(2(3x+1))*(3)*(3)

    You do not have to but I choose to simplify so

    f''(x)= 54(3x+1)
    Product rule? Why not just take the derivative of (3x + 1)^2 using a combination of the chain and power rules? (Like startingover did when (s)he took the derivative of (3x + 1)^3 in the second line.) Thinking of this in terms of the product rule is overkill.

    -Dan
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  5. #5
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    Re:

    Good point! Sorry for the overkill...
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