Question

Differentiate the given equation implicitly and then solve for y'
2x²- 6y - 12 = 0.

Answer 1

To differentiate the given equation implicitly, we find the derivative of each term and solve for y'. The result is y' = 2x/3.

Step-by-step explanation:

To differentiate the given equation implicitly, we need to find the derivative of both sides of the equation with respect to x. Let's differentiate each term one by one:

For the term 2x², the derivative with respect to x is 4x.

For the term -6y, the derivative with respect to x is -6y'.

For the constant term -12, the derivative with respect to x is 0.

So, after differentiating both sides, we have 4x - 6y' = 0.

Now, let's solve this equation for y':

6y' = 4x

y' = (4x)/6

y' = 2x/3