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Math Help - Calculus Problems. Chain rule, rate of change.

  1. #1
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    Calculus Problems. Chain rule, rate of change.

    Well I've been trying these problems for awhile, I'll type the problem out as well as what I have gotten as the answer and how I got there. Thanks for any help...my prof likes to throw things at us that is very challengin on HW..
    PROBLEM 1
    f(x)=1/(x-2x^2)^(9/8)
    Find the derivative of f(x).

    For starters i moved the binomial to the numerator and switched the power to negative giving me f(x)=(x-2x^2)^(-9/8) . After that I simply applied the chain rule giving me (-9/8)(x-2x^2)^-17/8(-4x) . It says this answer is incorrect...

    PROBLEM 2
    f(x)=sqrt(3+sqrt4x) The 4x has two sqrt over it. I broke this problem down to read f(x)=(3^1/2+4x^1/2)^1/2 . I then used the chain rule which gave me (1/2)(3^1/2+4x^1/2)(2x^-1/2) . It says this answer is incorrect...

    I'll post the other two up after I get some help on these because I havent even been able to start them. They are more difficult then these two. Thanks for the help.

    -Brad
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  2. #2
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    Quote Originally Posted by lmao View Post
    Well I've been trying these problems for awhile, I'll type the problem out as well as what I have gotten as the answer and how I got there. Thanks for any help...my prof likes to throw things at us that is very challengin on HW..
    PROBLEM 1
    f(x)=1/(x-2x^2)^(9/8)
    Find the derivative of f(x).

    For starters i moved the binomial to the numerator and switched the power to negative giving me f(x)=(x-2x^2)^(-9/8) . After that I simply applied the chain rule giving me (-9/8)(x-2x^2)^-17/8(-4x) . It says this answer is incorrect...
    f(x)=1/[(x - 2x^2)^(9/8)] = (x - 2x^2)^(-9/8)

    [(-9/8)*(x - 2x^2)^(-17/8)]*(1 - 4x)

    The result you have is close; you didn't take the derivative of x, and remember that you're then multiplying that term by the whole expression.
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  3. #3
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    Quote Originally Posted by lmao View Post
    PROBLEM 2
    f(x)=sqrt(3+sqrt4x) The 4x has two sqrt over it. I broke this problem down to read f(x)=(3^1/2+4x^1/2)^1/2 . I then used the chain rule which gave me (1/2)(3^1/2+4x^1/2)(2x^-1/2) . It says this answer is incorrect...

    I'll post the other two up after I get some help on these because I havent even been able to start them. They are more difficult then these two. Thanks for the help.

    -Brad
    First of all, f(x)=(3^1/2+4x^1/2)^1/2 is not equivalent to f(x)=sqrt(3+sqrt4x). I think you mean:

    (3 + (4x)^(1/2))^(1/2). Now this should be very easy.

    [(1/2)*[3 + (4x)^(1/2)]^(-1/2)]*[[(1/2)*(4x)^(-1/2)]*4]

    Voila.
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