Question

Find y" by implicit differentiation for the equation x² - 7y² = 7?

Answer 1

To find y" by implicit differentiation for the equation x² - 7y² = 7, differentiate both sides of the equation with respect to x using the chain rule and solve for y".

Step-by-step explanation:

To find y" by implicit differentiation for the equation x² - 7y² = 7, we need to differentiate both sides of the equation with respect to x using the chain rule. Let's go step by step:

1. Differentiate x² with respect to x to get 2x.
2. Differentiate -7y² with respect to x using the chain rule. The derivative of -7y² with respect to y is -14y. Then multiply it by the derivative of y with respect to x, which is y'.
3. Set the resulting expression equal to 0 to get the second derivative.
4. Solve for y" by isolating the y" term.

After following these steps, you should end up with the expression for y". Remember to simplify as much as possible.