Originally Posted by
mark1950 Thanks, Mr. Fantastic but I have a problem. Here is my take on the question :
I differentiate the whole thing to get,
$\displaystyle 4x - (x\frac{dy}{dx} + y) + 6y {\color{red} \frac{dy}{dx}} = 0 $ Mr F says: Note the correction in red (so all that follows is wrong). This follows from the chain rule.
$\displaystyle \frac{4x + 5y}{x} = \frac{dy}{dx} $
Then, I solved it to find the gradient :
$\displaystyle \frac{4(3) + 5(1)}{3} = \frac{dy}{dx} $
to get 17/3. Since they want me to find the normal, I solved the gradient to -3/17.
But when I try to find the equation, I got
17y = -3x + 26
which is way different then the answer, which is, 11y = 3x + 2. Am I wrong or is it the answer that's wrong? Thanks.