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What is the #100#th derivative of #2e^x#?

Answer 1

Isaiah Allen

Well, you should memorize that the derivative of #e^x# is #e^x#. Therefore, #(d^n)/(dx^n)[e^x] = f^((n))(x) = e^x#.

The constant floats out front, so

#(d^n)/(dx^n)[2e^(x)]#

#= 2(d^n)/(dx^n)[e^(x)]#

#= 2e^x#

Since we just proved it in general, what does that tell you about the #100#th derivative?

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Answer 2

Christopher Agresta

The 100th derivative of (2e^x) is (2e^x).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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