Question

Find the equation of the tangent line: yx^2+xy^2=6, (1, 2). Can anyone explain the steps of implicit differentiation?

Answer 1

y'x^2+y(2x)+x(2yy')+y^2=0

Answer 2

Thats the first step right?

Answer 3

y'(x^2+2xy)=-(2xy+y^2)
y'=-y(2x+y)/x(x+2y)

Answer 4

m=y'(at (1,2))=-6/5

Answer 5

tangent line is
y-2=-6/5(x-1)

Answer 6

On the key it says the slope is -8/5

Answer 7

oh mistake in computations

Answer 8

-8/5 is the right ans

Answer 9

So implicit differentiation, can you quickly verbally go through it, what steps do you do?

Answer 10

for yx^2
use product rule
(derivative of y)x^2+(derivative of x^2) y

Answer 11

y'x^2+2xy....clear?

Answer 12

similar for the second term

Answer 13

OHHHHH!!!! I SEEEEEEE!!!!

Answer 14

THANK YOU SO MUCH! I really appreciate it :D

Answer 15

u welcome:)