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Can anyone please explain why d/dx of e^x is still e^x? I am new in this calculas stuff. And this video doesn't explain anything at all. Please help. I have an exam coming. I don't want to fail. 😥
just look at the taylor series of e^x. you'll see that its derivative always remains the same.
There is a proof for it but you don't need to know it. Just remember d/dx*e^x=e^x. If you want to be more general you can think of it as d/dx of e^ax is ae^ax. Then use the chain rule if you have something like e^3x^2 the d/dx of that is (e^3x^2)*(2*3x). The more general term for e^ax^n using the chain rule is you set u=ax^n then du=nax^(n-1)dx then du/dx=nax^(n-1), so d/dx of e^ax^n turns into (d/du*e^u)*(du/dx). The d/du of e^u is e^u so this equals (e^u)*(nax^(n-1)), then you plug u=ax^n back
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