Final answer:
To find the derivative of y=log₄ (x−1)/(x+1)ˡⁿ⁴, we can use the logarithmic differentiation rule. Let's start by taking the natural logarithm of both sides. Then, we can differentiate both sides with respect to x using the chain rule and solve for y' to find the derivative.
Step-by-step explanation:
To find the derivative of y=log₄ (x−1)/(x+1)ˡⁿ⁴, we can use the logarithmic differentiation rule. Let's start by taking the natural logarithm of both sides:
ln(y) = ln(log₄ (x−1)/(x+1)ˡⁿ⁴)
Now, we can use the properties of logarithms to simplify the expression:
ln(y) = ln[(x−1)/(x+1)ˡⁿ⁴]
Next, we can differentiate both sides with respect to x using the chain rule:
(1/y) * y' = ((x+1)/(x-1)ˡⁿ⁴)' * ln(4)
We can solve for y' to find the derivative:
y' = [(x+1)/(x-1)ˡⁿ⁴]' * ln(4) * y
Finally, we can simplify the expression [(x+1)/(x-1)ˡⁿ⁴]' to get the derivative of y.