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How do you find the derivative of #f(x) = (x^3)(e^x)#?

Answer 1

Aurora Alvarado

#f'(x)=x^2e^x(3+x)#

You can use the Product Rule: #f(x)=h(x)g(x)# derived gives you: #f'(x)=h'(x)g(x)+h(x)g'(x)#

in your case: #f'(x)=3x^2e^x+x^3e^x=x^2e^x(3+x)#

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Answer 2

Charles Anctil

To find the derivative of $f(x) = x^3 e^x$ , you can use the product rule of differentiation, which states that the derivative of the product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.

Using this rule, the derivative of $f(x)$ is:

$f'(x) = (3x^2)(e^x) + (x^3)(e^x)$

Simplified, this becomes:

$f'(x) = 3x^2e^x + x^3e^x$

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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.