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What is the derivative of #e^xln2#?

Answer 1

#e^xln2#

First, note that

#d/dx(e^x)=e^x#

Next, recall that #ln2# is a constant, just like #2# or #-5#. This means it gets "carried along" with the differentiation and won't be modified. Thus,

#d/dx(e^xln2)=ln2d/dx(e^x)=e^xln2#

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Answer 2

Samantha Adkison

If there is a typo in the question and the intended question was for #e^(xln2)#

In this case, we are differentiating a function of the form #e^u#.

We'll use #d/dx(e^u) = e^u (du)/dx#.

Because #u=xln2# we need the same observation mason m made in the answer to the question as typed, that #ln2# is simply some constant, so #(du)/dx = d/dx(xln2) = ln2#

We get

#d/dx(e^(xln2) )= e^(xln2)ln2#.

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Answer 3

Emily Ammerman

The derivative of ( e^{x\ln 2} ) is ( (\ln 2) \cdot e^{x\ln 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.