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avatarPistacheRose369
Postsecondary • 2mo.

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:

image.png

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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!

Mathematics
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      avatarCitrineCandide143teacher check
      Team Alloprof • 2mo.

      Hi PistacheRose369,

      Thanks for using our service.

      Our service is for student in high school.

      I'm sorry, I can't help your more.

      Have a great night!

      Lea-Kim

    Québec RioTinto Desjardins Pathy TROTTIER OTHER
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