Final answer:
To find the second derivative of the equation x² - 4y² = 9, differentiate the equation twice with respect to x.
Step-by-step explanation:
To find the second derivative of the equation x² - 4y² = 9, we need to differentiate the equation twice with respect to x. Let's start by differentiating it once:
2x - 8yy' = 0
Now, let's differentiate it again:
2 - 8(y')² - 8yy'' = 0
Simplifying gives us:
8(y')² + 8yy'' = 2
Dividing both sides by 8:
(y')² + yy'' = 1/4
So, the second derivative for x² - 4y² = 9 is yy'' + (y')² = 1/4.