# Differentiation and Implicit Differentiation

• Feb 6th 2009, 01:23 AM
katieeej
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)

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

thanks sososososoos much!!!!!!!!!
• Feb 6th 2009, 04:07 AM
earboth
Quote:

Originally Posted by katieeej
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

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:

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

Collect all terms containing y' at the LHS:

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