Final answer:
To find the derivative of the function y = ln(x√(x² – 4)), we can use the chain rule. The derivative is 1/x + 1/√(x² – 4) * x.
Step-by-step explanation:
To find the derivative of the function y = ln(x√(x² – 4)), we can use the chain rule. First, let's rewrite the function as the product of two functions: y = ln(x) + ln(√(x² – 4)). The derivative of ln(x) is 1/x, and the derivative of ln(√(x² – 4)) can be found using the chain rule. Let's denote √(x² – 4) as u. The derivative of ln(u) is 1/u times the derivative of u. Therefore, the derivative of ln(√(x² – 4)) is 1/√(x² – 4) * (1/2) * 2x. Combining the derivatives, we get: dy/dx = 1/x + 1/√(x² – 4) * x.