Question

Consider the following equation.

3x^2 - y^2 = 5

(a) Find
y'
by implicit differentiation.

(b) Solve the equation explicitly for y and differentiate to get
y'
in terms of x.

Answer 1

Ah, I got it. derivative both sides, 6x - 2y y' =0
2yy' = 6
x y' = 6x/2y = 3x/y
this is implicit derivative

Answer 2

this is explicit derivative:
3x^2 - y^2 =5
y^2 = 3x^2 -5
\[y = \pm\sqrt{3x^2 -5}\]
take derivative both sides to get the answer.

Answer 3

Thank you!