How do you use the chain rule to differentiate #y = e^lnx#?

Answer 1

#dy/dx = e^lnx/x = 1#

Let #y = e^u# and #u = lnx#
Then #y' = e^u xx 1/x = e^lnx xx 1/x = e^lnx/x = 1#

Hopefully this helps!

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Answer 2

#f'(x) =1#

#f(x) = e^lnx = x#
#f'(x) = d/dx (x) = 1# (No need of the Chain rule)

However, since the question askes that we use the Chain rule:

#f(x) = e^lnx# #f'(x) = e^lnx * 1/x# (Standard differentials and Chain rule)
#= x*1/x = 1#
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Answer 3

To differentiate ( y = e^{\ln(x)} ) using the chain rule, first recognize that ( e^{\ln(x)} ) is simply ( x ) because ( e ) and ( \ln ) are inverse functions. So, the derivative of ( y = e^{\ln(x)} ) with respect to ( x ) is the derivative of ( x ) with respect to ( x ), which equals ( 1 ). Thus, ( \frac{dy}{dx} = 1 ).

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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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