Differentiate the function.f(x) = ln(x7 + 4)f '(x) =

To differentiate the function f(x) = ln(x^7 + 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.

Step 1: Identify the outer and inner functions. Here, the outer function is ln(x) and the inner function is x^7 + 4.

Step 2: Differentiate the outer function. The derivative of ln(x) is 1/x.

Step 3: Differentiate the inner function. The derivative of x^7 + 4 is 7x^6.

Step 4: Apply the chain rule. The derivative of the function is the derivative of the outer function times the derivative of the inner function.

So, f'(x) = (1/(x^7 + 4)) * 7x^6 = 7x^6 / (x^7 + 4).