Hello,
I have a question about the derivative of an exponential function. Here's a picture of the tangeant line passing through point (0,1) in a zoomed in exponential function:
I'm honestly a little confused about what's happening in the picture.
1) Why do we write the vertical variation (dy) as "1 ⋅ dx"?? Where does this come from?
2) I don't understand what the equation highlighted in blue represents exactly. What is "e^dx"? And, why is it equal to "1+dx"??
3) Lastly, I'm not sure to understand why, when working with derivatives, we want the initial slope of an exponential function to be equal to 1. Is there a particular reason for this?
I'm a very visual person, so it would really help me out if I could be provided with illustrations and calculations along the explanations.
Thank you so much for your help!
Explanation (1)
Student Explanation
September 11, 2025
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