Question

Consider the following equation. 9x2 − y2 = 6 (a) Find y' by implicit differentiation. y' = (b) Solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ±

Answer 1

Answer:

Step-by-step explanation:

Given is an equation in x and y as

$9x^2 - y^2 = 6$

We use implicit method to differentiate the above equation

18x-2yy'=0

y' = 9x/y

b) to solve the equation explicitly for y and differentiate to get y' in terms of x. y' = ±

We separate the variables as

$yy' =9x\\\frac{y^2}{2} =\frac{9x^2}{2} +C\\y^2 =9x^2+2C$

Take square root

$y=\sqrt{9x^2+2C} \\y=-\sqrt{9x^2+2C}$