Evaluate the derivative of f(x) = e^x + ln(x) at x = 1.
Practice Questions
Q1
Evaluate the derivative of f(x) = e^x + ln(x) at x = 1.
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Questions & Step-by-Step Solutions
Evaluate the derivative of f(x) = e^x + ln(x) at x = 1.
Step 1: Identify the function we need to differentiate, which is f(x) = e^x + ln(x).
Step 2: Find the derivative of f(x). The derivative of e^x is e^x, and the derivative of ln(x) is 1/x.
Step 3: Combine the derivatives to get f'(x) = e^x + 1/x.
Step 4: Now, we need to evaluate the derivative at x = 1. Substitute 1 into the derivative: f'(1) = e^1 + 1/1.
Step 5: Simplify the expression: f'(1) = e + 1.
Derivative of Exponential and Logarithmic Functions – The question tests the ability to differentiate the exponential function e^x and the natural logarithm ln(x), as well as evaluating the derivative at a specific point.
