Find the derivative of the following function.𝑦=ln(8−𝑥4)𝑑𝑦𝑑𝑥=

To find the derivative of the function y = ln(8 - x^4), we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Here are the steps:

1. Identify the outer function and the inner function. In this case, the outer function is ln(x) and the inner function is 8 - x^4.

2. Find the derivative of the outer function. The derivative of ln(x) with respect to x is 1/x.

3. Find the derivative of the inner function. The derivative of 8 - x^4 with respect to x is -4x^3.

4. Apply the chain rule. The derivative of the function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.

So, dy/dx = (1/(8 - x^4)) * (-4x^3)

Therefore, the derivative of the function y = ln(8 - x^4) is dy/dx = -4x^3 / (8 - x^4).