How do you find the derivative of #f(x) = x^3e^x#?
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To find the derivative of ( f(x) = x^3e^x ), you can use the product rule. The product rule states that if you have two functions, ( u(x) ) and ( v(x) ), then the derivative of their product is given by ( \frac{d}{dx}(u(x)v(x)) = u'(x)v(x) + u(x)v'(x) ). Applying the product rule to ( f(x) = x^3e^x ), where ( u(x) = x^3 ) and ( v(x) = e^x ), we get:
[ f'(x) = (3x^2)e^x + x^3(e^x) ]
[ f'(x) = 3x^2e^x + x^3e^x ]
So, the derivative of ( f(x) = x^3e^x ) is ( f'(x) = 3x^2e^x + x^3e^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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