If y=8ln8x𝑦=8𝑙𝑛8𝑥, find dydx.

To find the derivative of the function y = 8ln(8x), 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.

Step 1: Identify the outer and inner functions. Here, the outer function is y = 8ln(u) and the inner function is u = 8x.

Step 2: Find the derivative of the outer function. The derivative of y = ln(u) is 1/u. So, the derivative of y = 8ln(u) is 8/u.

Step 3: Find the derivative of the inner function. The derivative of u = 8x is 8.

Step 4: Apply the chain rule. The derivative of the composite function is the product of the derivatives of the outer and inner functions. So, dy/dx = (8/u) * 8 = 64/u.

Step 5: Substitute the inner function back into the derivative. So, dy/dx = 64/(8x) = 8/x.