f(x) = ln(x7 + 4)f '(x)
Solution
To find the derivative of 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: Find the derivative of the outer function. The derivative of ln(x) is 1/x. So, the derivative of the outer function is 1/(x^7 + 4).
Step 3: Find the derivative of the inner function. The derivative of x^7 + 4 is 7x^6.
Step 4: Multiply the derivatives of the outer and inner functions. So, the derivative of the function f(x) = ln(x^7 + 4) is f'(x) = (1/(x^7 + 4)) * 7x^6 = 7x^6 / (x^7 + 4).
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