# If #f(x) =xe^x# and #g(x) = sin3x #, what is #f'(g(x)) #?

I think you meant to write this as: what is

Putting these things together leads to the final answer:

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To find ( f'(g(x)) ), first, find ( g'(x) ). Then substitute ( g(x) ) into ( f'(x) ).

( g'(x) = 3 \cos(3x) )

Now, substitute ( g(x) ) into ( f'(x) ):

( f'(g(x)) = e^{g(x)}(1+g(x)) )

Substitute ( g(x) = \sin(3x) ) into the above expression:

( f'(g(x)) = e^{\sin(3x)}(1+\sin(3x)) )

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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.

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