# Implicit differetiation

1. May 24, 2012

### ericndegwa

1. The problem statement, all variables and given/known data

find dy/dx if x=1/1 + t and y = t2/1 + t

2. Relevant equations

dy/dx = (dy/dt) / (dx/dt)

3. The attempt at a solution

dx/dt = 1 * (1 + t )^-1

dx/dt = -1/ (1 +t)^2

dy/dt = t^2 * (1 +t)^-1

dy/dt = -2t/(1+ t)^2

therfore dy/dx = -2t/(1 + t)^2 / -1/(1 + t)^2

2t

2. May 24, 2012

### sharks

Your equations aren't clear. Edit your post to fix them or just attach a picture/screenshot.

x=1/1 + t meaning x= 1 +t ? or x= 1/ (1+t) ? (hence the importance of using parentheses!)

y = t2/1 + t

dy/dt = t^2 * (1 +t)^-1 ? So, y = t^2/1 + t ?

3. May 24, 2012

### Staff: Mentor

look at dy/dt again its not just 2 t/ (1+t) there's a term missing assuming that y=t^2 /(1+t)

4. May 24, 2012

### Staff: Mentor

Aside from the missing parentheses that have already been mentioned, you are showing equations that are incorrect. The first and third equations above are x and y, respectively, not dx/dt and dy/dt.

In calculating dy/dt, you need to use either the product rule (on t2(1 + t)-1) or the quotient rule (on t2/(1 + t) ).