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Math Help - Differentiation and Implicit Differentiation

  1. #1
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    Differentiation and Implicit Differentiation

    implicit differentiation

    1) y=x^2+yx
    2) xy-y^3=1
    3) 1/xy-y^2=2

    differentiation
    1) f(x)=<square root>(x^2-1)/ 1+<square root>(x^2+1)

    please find
    1) d/dx <square root> f(x)+g(x)

    thanks sososososoos much!!!!!!!!!
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  2. #2
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    Quote Originally Posted by katieeej View Post
    implicit differentiation

    1) y=x^2+yx
    2) xy-y^3=1 ........ Use product rule and chain rule
    3) 1/xy-y^2=2 ........ Use quotient rule and chain rule

    differentiation
    1) f(x)=<square root>(x^2-1)/ 1+<square root>(x^2+1) ........ Use quotient rule and chain rule


    please find
    1) d/dx <square root> f(x)+g(x) ........ Use chain rule


    thanks sososososoos much!!!!!!!!! Are you sure your keyboard is working correctly?
    I'll show you how to do the first example. I leave the following questions for you. I've mentioned above what you should do with the other questions.

    to #1: Use product rule with the second summand:

    y=x^2+yx~\implies~ y'=2x+(y+x\cdot y')

    Collect all terms containing y' at the LHS:

    y'-x \cdot y' = 2x+y ~\implies~y'(1-x)=2x+y~\implies~ y'=\dfrac{2x+y}{1-x}
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