Respuesta :
Answer:
Step-by-step explanation:
Given is an equation in x and y as
[tex]9x^2 - y^2 = 6[/tex]
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
[tex]yy' =9x\\\frac{y^2}{2} =\frac{9x^2}{2} +C\\y^2 =9x^2+2C[/tex]
Take square root
[tex]y=\sqrt{9x^2+2C} \\y=-\sqrt{9x^2+2C}[/tex]
The value of y' by implicit differentiation is 9x/y and the value of y is [tex]\pm \sqrt{9x^2 + 2C}\\[/tex].
What is implicit differentiation?
We differentiate each side of an equation with two variables by taking one as a variable and the rest are constant.
Given
The function is [tex]\rm 9x^2 - y^2 = 6[/tex].
where x and y are variables.
a. The function is [tex]\rm 9x^2 - y^2 = 6[/tex].
On differentiating the equation, we have
[tex]\rm 18x - y y' = 0\\[/tex]
on simplifying, we have
[tex]\rm y' = \dfrac{9x }{y}[/tex]
b. To solve the equation explicitly for y and differentiate to get y' in terms of x.
[tex]\rm y' = \dfrac{9x }{y}[/tex]
Separate the variables
[tex]\rm yy' = 9x\\\\\dfrac{y^2}{2} = \dfrac{9x^2}{2} + C\\\\y^2 = \9x^2 + 2C[/tex]
Taking square root on both the side
[tex]\rm y = \pm \sqrt{9x^2 + 2C}\\[/tex]
More about the implicit differentiation link is given below.
https://brainly.com/question/20319481
