Learn how to find the derivative of log x. The derivative is d/dx[log x].
Below is the graph of f(x) = log x and its derivative f'(x). Notice how the original function and derivative relate to each other.
Original Function:
Derivative:
This derivative represents the rate of change of the original function. The calculation follows standard differentiation rules as shown in the step-by-step solution below.
To differentiate log x, we first recognize that it has the form of a power function. The Power Rule is applied here because the natural logarithm, log x, can be treated as a function of the form x^n where n = 1.
💡 Why this works: The Power Rule is appropriate because the logarithmic function shares characteristics with power functions, which involve exponentiation and differentiation with respect to a base.
The Power Rule states that for a function of the form x^n, the derivative is n * x^(n-1). For log x, we treat the function as x^1, so the derivative becomes 1 * x^(1-1), which simplifies to 1/x.
💡 Why this works: By applying the Power Rule, we differentiate log x to obtain 1/x, reflecting the rate of change of the logarithmic function with respect to x.
The application of the Power Rule results in the derivative of log x, which is 1/x. This simplified form is the final result, and it represents the slope of the logarithmic function at any point on its curve.
💡 Why this works: Since the Power Rule has been correctly applied, the derivative of log x is confirmed to be 1/x, which is the correct and simplified result for this function.
[Teaching explanation - to be filled]
[Application to this function - to be filled]
❌ Common Mistake:
Not simplifying the final answer
✅ Correct Approach:
Always simplify your derivative to its most reduced form
Double-check your work by comparing your steps with our solution. Use our calculator to verify each step of the differentiation process.
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