Question

Find the second derivative for x² - 4y² = 9.
a) -4y
b) 4y
c) -2y
d) 2y

Answer 1

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.