# Implicit differentiation problem

• Feb 6th 2009, 12:07 PM
gracey
Implicit differentiation problem
Find dy/dx in terms of x and y

ln(x²+1) + ln(y+1) = x + y

thanks any help is fab (Thinking)
• Feb 6th 2009, 12:13 PM
running-gag
Quote:

Originally Posted by gracey
Find dy/dx in terms of x and y

ln(x²+1) + ln(y+1) = x + y

thanks any help is fab (Thinking)

Hi

I would simply take the derivative (with respect to x) of the equality

$\frac{2x}{x^2+1} + \frac{y'}{y+1} = 1 + y'$
• Feb 6th 2009, 12:22 PM
Soroban
Hello, gracey!

Quote:

Find $\frac{dy}{dx}$ in terms of $x\text{ and }y$

. . $\ln(x^2+1) + \ln(y+1) \:=\: x + y$

Differentiate implicitly and solve for $\frac{dy}{dx}$

. . $\frac{2x}{x^2+1} + \frac{\frac{dy}{dx}}{u+1} \:=\:1 + \frac{dy}{dx}$ . . . .
did you get this far?

The rest is just algebra . . .