Question

find dy/dx by implicit differentation x^2+xy-y^2=4

Answer 1

(x^2) ' + (xy)' -(y^2)' =0

Answer 2

(xy) ' product rule:
x' *y + x *y'
x' is just 1, so
y+ x* y '

Answer 3

try (y^2)' ... use the chain rule..

Answer 4

yeah its 2y*y'

Answer 5

yes

Answer 6

2x + y+ x* y ' +2y* y' =0

Answer 7

solve for y ' algebraically...

Answer 8

factor out y'

Answer 9

yeah, move the 2x and the y to the other side and then factor y ' out of the remaining terms..

Answer 10

so it would be -2x-y in the numerator?

Answer 11

is -2x-y the same as 2y+y?

Answer 12

yes it's the numerator

Answer 13

first find value of first derivative and arrange equation take dy/dx next to one another take commondy/dx and take the other value to other side