If f(x) = e^x, what is the value of f''(0)? (2021)

If f(x) = e^x, what is the value of f''(0)? (2021)

Step 1: Identify the function given in the question, which is f(x) = e^x.
Step 2: Find the first derivative of the function, f'(x). The derivative of e^x is e^x, so f'(x) = e^x.
Step 3: Find the second derivative of the function, f''(x). The derivative of f'(x) = e^x is also e^x, so f''(x) = e^x.
Step 4: Evaluate the second derivative at x = 0. Substitute 0 into f''(x): f''(0) = e^0.
Step 5: Calculate e^0. The value of e^0 is 1.
Step 6: Conclude that f''(0) = 1.

Differentiation of Exponential Functions – Understanding how to differentiate the exponential function f(x) = e^x and apply it to find higher-order derivatives.
Evaluation of Functions at Specific Points – Evaluating the second derivative at a specific point, in this case, x = 0.