# How do you differentiate #(x^2) (sin x)#?

By using the product rule.

Using the rule of product:

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To differentiate the expression ( x^2 \cdot \sin(x) ), you can use the product rule, which states:

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

Let ( f(x) = x^2 ) and ( g(x) = \sin(x) ).

Now, find the derivatives of ( f(x) ) and ( g(x) ):

For ( f(x) = x^2 ): [ f'(x) = 2x ]

For ( g(x) = \sin(x) ): [ g'(x) = \cos(x) ]

Now, apply the product rule:

[ \frac{d}{dx}(x^2 \cdot \sin(x)) = (2x) \cdot (\sin(x)) + (x^2) \cdot (\cos(x)) ]

[ = 2x \sin(x) + x^2 \cos(x) ]

So, the derivative of ( x^2 \cdot \sin(x) ) is:

[ \frac{d}{dx}(x^2 \cdot \sin(x)) = 2x \sin(x) + x^2 \cos(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.

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