Problem finding normal line equation using partial derivative and gradient vector
I'm trying to solve a problem but the answer is different from the book.
So wondering what am i doing wrong. The problem is like this:
Find equations for the lines that are normal to function:
The way i did was first find the gradient vector:
Then get the derivative which is(because we know that slope
of a function is it's derivative at that point):
Finally the equation of normal line is:
Is this right or am i wrong? The answer back of my book is
Why book's answer is different? Any ideas?