How do you find the derivative of #y=e^x#?

Answer 1
This is one of the favorite function to take the derivatives of. #y'=e^x#
If you wish to find this derivative by the limit definition, then here is how we find it. First, we have to know the following property of #e#: #lim_{h to 0}{e^h-1}/{h}=1#. (Note: This means that the slope of #y=e^x# at #x=0# is #1#.)
By the limit definition of the derivative, we have #y'=lim_{h to 0}{e^{x+h}-e^x}/h =lim_{h to 0}{e^x cdot e^h-e^x}/h# by factoring out #e^x#, #=lim_{h to 0}{e^x(e^h-1)}/h=e^x lim_{h to 0}{e^h-1}/h# by the property of #e# mentioned above, #=e^x cdot 1=e^x#
Hence, the derivative of #e^x# is itself.
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Answer 2

To find the derivative of ( y = e^x ), you can use the fact that the derivative of ( e^x ) with respect to ( x ) is simply ( e^x ). So, the derivative of ( y = e^x ) is ( \frac{dy}{dx} = e^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.

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.

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.

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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