# Thread: Implicit Differentiation

1. ## Implicit Differentiation

First time using LaTeX. Found it to be quick and easy on the eyes.

1) If $cos x = e^y$ and x is greater than zero and less than pi, what is $dy/dx$ in terms of x.

my steps
-take the derivative of both sides $-sinx=e^y (dy/dx)$

-this is where i am lost. I think I should take the ln of each side but i am not sure. All help is appreciated.

2. Originally Posted by dandaman
First time using LaTeX. Found it to be quick and easy on the eyes.

1) If $cos x = e^y$ and x is greater than zero and less than pi, what is $dy/dx$ in terms of x.

my steps
-take the derivative of both sides $-sinx=e^y (dy/dx)$

-this is where i am lost. I think I should take the ln of each side but i am not sure. All help is appreciated.
$cos x = e^y$

Differentiate both sides

(cosx) ' = (e^y)'

(cosx) ' = -sinx *(x)' = -sinx -- chain rule

(e^y)'= e^y * y' -- chain rules

-sinx = (e^y) y'

y' = -sinx /(e^y)

3. Originally Posted by dandaman
First time using LaTeX. Found it to be quick and easy on the eyes.

1) If $cos x = e^y$ and x is greater than zero and less than pi, what is $dy/dx$ in terms of x.

my steps
-take the derivative of both sides $-sinx=e^y (dy/dx)$

-this is where i am lost. I think I should take the ln of each side but i am not sure. All help is appreciated.
Note that your work leads to $\frac{\,dy}{\,dx}=-\frac{\sin x}{e^y}$

But what did we say $e^y$ originally was? (That's my BIG hint)

Can you take it from here?

4. OHHHHH... Thanks a ton you two... That was a good hint also... Thanks thanks thanks