Learn how to find the derivative of ln x. The derivative is d/dx[ln x].
Below is the graph of f(x) = ln 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.
ln x is a logarithmic function with the base 'e', and it requires the Power Rule for differentiation. Recognizing its form helps in choosing the appropriate rule.
💡 Why this works: The natural logarithm ln x has a unique structure that leads to the application of the Power Rule for derivatives. The function is a logarithmic expression, and it directly follows the general rule for differentiating ln x.
The Power Rule states that the derivative of ln x is the inverse of x, or 1/x. Applying this rule results in d/dx[ln x] = 1/x.
💡 Why this works: By applying the Power Rule to ln x, we differentiate it and simplify the expression, arriving at the derivative as 1/x. This reflects how the function grows as x changes.
After applying the Power Rule, we verify the result and simplify it to obtain the final form of the derivative: d/dx[ln x] = 1/x.
💡 Why this works: The simplified result confirms that the derivative of ln x is indeed 1/x. This matches the expected outcome for logarithmic differentiation.
[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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