# Math Help - Implicit & Exponential Differentiation

1. ## Implicit & Exponential Differentiation

Can anyone tell me how I have done with these ones on Implicit & Exponential Differentiation?

2. a)

$x^2 + y^2 - 2x - 6y + 5 = 0$

Now we differentiate it implicitly:

$2x + 2yy' - 2 - 6y' = 0$

$2yy' - 6y' = -2x + 2$

$y'(2y - 6) = 2x + 2$

$y' = \frac{2x + 2}{2y - 6}$

b)

$x^2 + 2xy + 3y^2 = 4$

Implicitly:

$2x + (2y + 2xy') + 6yy' = 0$

$2x + 2y + 2xy' + 6yy' = 0$

$2xy' + 6yy' = -2x - 2y$

$y'(2x + 6y) = -2x - 2y$

$y' = \frac{-x - y}{x + 3y}$

With this you are forgetting that when you differentiate y in terms of x then you must do something along the lines of:

$\frac{dy}{dx}[y^2] = 2y\frac{dy}{dx}$

$=2yy'$