For the function f(x) = e^x, what is f''(x)? (2021)
Practice Questions
Q1
For the function f(x) = e^x, what is f''(x)? (2021)
e^x
xe^x
0
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Questions & Step-by-Step Solutions
For the function f(x) = e^x, what is f''(x)? (2021)
Step 1: Start with the function f(x) = e^x.
Step 2: Find the first derivative f'(x) by differentiating e^x. The derivative of e^x is e^x.
Step 3: Now, we have f'(x) = e^x.
Step 4: Find the second derivative f''(x) by differentiating f'(x) = e^x again. The derivative of e^x is still e^x.
Step 5: Therefore, f''(x) = e^x.
Differentiation of Exponential Functions – Understanding how to differentiate the exponential function e^x, which is unique in that its derivative is itself.
Higher Order Derivatives – Recognizing that the second derivative of e^x is the same as the first derivative, illustrating the properties of exponential functions.
