# What is the derivative of #(3x^3)/e^x#?

Thus...

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To find the derivative of the function (\frac{3x^3}{e^x}), you can use the quotient rule, which states that if you have a function in the form (f(x) = \frac{g(x)}{h(x)}), then its derivative is given by:

[f'(x) = \frac{g'(x) \cdot h(x) - g(x) \cdot h'(x)}{[h(x)]^2}]

Applying the quotient rule to the given function, where (g(x) = 3x^3) and (h(x) = e^x):

[g'(x) = 9x^2] [h'(x) = e^x]

Therefore, the derivative of the function (\frac{3x^3}{e^x}) is:

[f'(x) = \frac{(9x^2)(e^x) - (3x^3)(e^x)}{(e^x)^2} = \frac{9x^2e^x - 3x^3e^x}{e^{2x}}]

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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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