# How do you find the derivative of #f(x) = x^2 (x-5)^3#?

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To find the derivative of ( f(x) = x^2 (x-5)^3 ), you can use the product rule:

[ \frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x) ]

Where ( f(x) = x^2 ) and ( g(x) = (x-5)^3 ).

Now, apply the product rule:

[ f'(x) = \frac{d}{dx}(x^2) = 2x ] [ g'(x) = \frac{d}{dx}[(x-5)^3] = 3(x-5)^2 ]

Therefore, the derivative of ( f(x) ) with respect to ( x ) is:

[ f'(x) = 2x \cdot (x-5)^3 + x^2 \cdot 3(x-5)^2 ]

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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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