How do you differentiate # y=(e^x)(lnx)#?
product rule
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To differentiate ( y = (e^x)(\ln x) ), you can use the product rule of differentiation. The product rule states that if ( y = u \cdot v ), then ( y' = u'v + uv' ).
Let ( u = e^x ) and ( v = \ln x ). Then, ( u' = e^x ) (since the derivative of ( e^x ) is itself) and ( v' = \frac{1}{x} ) (since the derivative of ( \ln x ) is ( \frac{1}{x} )).
Applying the product rule:
[ y' = (e^x)(\frac{1}{x}) + (e^x)(\ln x) ]
Thus, the derivative of ( y = (e^x)(\ln x) ) is:
[ y' = e^x \cdot \frac{1}{x} + e^x \cdot \ln x ]
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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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