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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- Feb 6th 2009, 01:23 AMkatieeejDifferentiation 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!!!!!!!!! - Feb 6th 2009, 04:07 AMearboth
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:

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

Collect all terms containing y' at the LHS:

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