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What is the derivative of #ln e^(2x)#?

Answer 1

Aurora Alvarado

#y=ln(u)#

#:. dy/(du)=1/u=1/(e^(2x))#

#u=e^(2x)#, #:. (du)/(dx)=2e^(2x)#

Now, using the chain rule...

#(dy)/(du)*(du)/(dx)=1/(e^(2x))*2e^(2x)=2#

#:. (dy)/(dx)=2#

This all worked because:

When #y=e^(f(x))#

#(dy)/(dx)=f'(x)e^(f(x))#

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Answer 2

Christopher Agresta

The derivative of ( \ln(e^{2x}) ) is ( \frac{d}{dx}(2x) ), which simplifies to ( 2 ).

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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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