Also can I get some help with this LONG, TIRESOME PROBLEM?

Find the derivative using the chain rule.
f(x)= ((3x-7)/(6x+3))^4

Thanks a lot!

(68/(12x^2+12x+3))*[(3x-7)/(6x+3)]^3

you should double check the answer
multiply 4((3x-7)/(6x+3))^3 by the derivative of (3x-7)/(6x+3), which you can find using the quotient rule

that was so right!! thank you so much, i really appreciate all your help!

Yes, the quotent rule is the way to go. You previously asked to use the chain rule, a onerous, tiresome way.

To find the derivative of the given function using the chain rule, you need to follow these steps:

1. Start by considering the function: f(x) = ((3x - 7) / (6x + 3))^4.

2. Identify the inner function: u = (3x - 7) / (6x + 3).

3. Determine the outer function: y = u^4.

4. Differentiate the outer function with respect to the inner function using the power rule: dy/du = 4u^3.

5. Differentiate the inner function using the quotient rule: du/dx = [(6x + 3)(3) - (3x - 7)(6)] / (6x + 3)^2.

6. Combine the derivatives to find the derivative of the entire function: dy/dx = (dy/du) * (du/dx).

Substituting the derivatives obtained in steps 4 and 5 into step 6, the derivative of f(x) is given by:

dy/dx = 4u^3 * [(6x + 3)(3) - (3x - 7)(6)] / (6x + 3)^2.

Simplifying this expression further yields:

dy/dx = (68 / (12x^2 + 12x + 3)) * ((3x - 7) / (6x + 3))^3.

Please note that it is always recommended to double-check your answer to ensure accuracy.