Question

Find the derivative of the following:

1=x^2+4xy+4y

My answer is 2x. Is this correct?

Answer 1

Also, solve: ln(x^2-5)=0

take e of both sides

x^2-5=1

x^2=6

x=sqrt6 Is this correct?

Answer 2

to find the derivative of 1=x^2+4xy+4y
I have to know if you are finding dy/dx or not
if so, then you have to use implicit differentiation

0 = 2x + 4x(dy/dx) + 4y + 4dy/dx
-2x - 4y = dy/dx(4x + 4)
dy/dx = (-2x-4y)/(4x+4)
= -(x+2y)/(2x+2)

for the last, you should have
x = ± √6

remember , we cannot take ln or log of a negative, but since the x is squared first, both ±√6 will work