Final answer:
To find the derivative of y = ln(((6x + 16)¹⁴ * (8x - 6)³) / ((16x - 12)⁵ * (16x + 21)³)) with respect to x, use the chain rule and logarithmic differentiation.
Step-by-step explanation:
The derivative of y = ln(((6x + 16)¹⁴ * (8x - 6)³) / ((16x - 12)⁵ * (16x + 21)³)) with respect to x can be found using the chain rule and logarithmic differentiation.
- Apply the logarithmic differentiation rule: Take the natural logarithm of both sides of the equation.
- Use the properties of logarithms to simplify the expression.
- Apply the chain rule to differentiate the simplified expression.
- Simplify the result.
After following these steps, the derivative of y with respect to x can be found.