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Applied Calculus

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Find the first and second derivative of the function:
x/(7x+10)

Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first derivative to be 10/(7x+10)^2

  • Applied Calculus - ,

    I agree with your first derivative.

    Now, start with 10/(7x+10)^2 and take the derivative again.

    Denom times deriv of numerator = 0
    since deriv of 10 = 0

    minus the numer time the deriv of the denomin.
    - 10(2(7x+10)7) this is the chain rule
    You need to simplify this expression

    all over the denominator squared which makes the denominator to the 4th power.

  • Applied Calculus - ,

    y=x/(7x+10)

    y'=1/( ) - 7x/( )^2
    = (7x+10)x - 7x)/ (7x+10)^2

    and that is not equal to your answer.
    = (7x^2 +3x)/(7x+10)^2

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