Question

Search topics and skills ining Assessment Analytics Math Recommendations M.1 Find derivatives using implicit differentiation HvQ Find the derivative of y with respect to x. -17=5y³+4x³-9x²+9x

Answer 1

To find the derivative of y with respect to x using implicit differentiation, differentiate each term separately and treat y as an implicit function of x. The derivative is 0 = 15y² * dy/dx + 12x² - 18x + 9.

Step-by-step explanation:

To find the derivative of y with respect to x using implicit differentiation, we need to differentiate each term separately and treat y as an implicit function of x. Let's go through the steps:

1. Differentiate 5y³ with respect to x: The derivative of y³ is 3y² multiplied by the derivative of y with respect to x.
2. Differentiate 4x³ with respect to x: The derivative of x³ is 3x² multiplied by the derivative of x with respect to x.
3. Differentiate -9x² with respect to x: The derivative of -9x² is -18x multiplied by the derivative of x with respect to x.
4. Differentiate 9x with respect to x: The derivative of 9x is 9 multiplied by the derivative of x with respect to x.

Combining all these derivative terms, we get:

0 = 15y² * dy/dx + 12x² - 18x + 9

This is the derivative of y with respect to x.