Question

Find yʹ by implicit differentiation.
eˣ / y=2 x-6 y

Answer 1

To find yʹ by implicit differentiation, differentiate both sides of the equation using the quotient and product rules, set the expressions equal to each other, and solve for yʹ.

Step-by-step explanation:

To find yʹ by implicit differentiation, we need to differentiate both sides of the equation eˣ / y=2 x-6 y. Let's differentiate step by step:

1. Using the quotient rule, differentiate the left side: (eˣyʹ - eˣ yʹ) / y².
2. Using the product rule, differentiate the right side: 2 + (2x-6)yʹ.
3. Set the differentiated expressions equal to each other: (eˣyʹ - eˣ yʹ) / y² = 2 + (2x-6)yʹ.
4. Now, we can solve for yʹ by isolating it: move the terms with yʹ to one side and the other terms to the other side.
5. Finally, simplify the expression for yʹ to get your answer.