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

Answer 1

William Abdalla

The derivative of y = #xe^x# is y' = #e^x + xe^x#

Use the product rule (u'v + v'u) to calculate the derivative:

First, write the values of u, u', v and v':

u = #x# u' = 1 v = #e^x# v' = #e^x#

Next, substitute these values into the product formula:

(u'v + v'u)

(1 x #e^x#) + (#e^x# x #x#) = #e^x# + #xe^x#

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Answer 2

Luke Alvarez

To find the derivative of (y = xe^x), use the product rule, which is ((uv)' = u'v + uv'), where (u = x) and (v = e^x).

Differentiate (u = x): [u' = 1]

Differentiate (v = e^x): [v' = e^x]

Apply the product rule: [y' = u'v + uv' = (1)(e^x) + (x)(e^x) = e^x + xe^x]

So, the derivative of (y = xe^x) with respect to (x) is (y' = e^x + xe^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.