117k views
3 votes
Find dy/dx in terms of x and y if x3y−x−8y−15=0.

1 Answer

5 votes

Final answer:

To find dy/dx in terms of x and y, we use implicit differentiation. Applying the product rule and power rule, we differentiate both sides of the equation x^3y - x - 8y - 15 = 0 with respect to x. The resulting derivative equation is dy/dx = (8 - 3x^2y) / (x^3 - 8).

Step-by-step explanation:

To find dy/dx in terms of x and y, we will use implicit differentiation. Given the equation x^3y - x - 8y - 15 = 0, we will differentiate both sides with respect to x.

For the left side, we will use the product rule and the power rule. The derivative of x^3y with respect to x is 3x^2y + x^3(dy/dx). The derivative of -8y is -8(dy/dx). And the derivative of -15 with with respect to x is 0.

So, our derivative equation is: 3x^2y + x^3(dy/dx) - 8(dy/dx) = 0. Solving this equation for dy/dx gives us: dy/dx = (8 - 3x^2y) / (x^3 - 8).

User Rajiv Makhijani
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories