# How do you find the derivative of #(3x-2)^10 * (5x^2-x+1)^12#?

In this way:

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To find the derivative of the given function, you would use the product rule and chain rule.

The derivative of the function ( (3x-2)^{10} \cdot (5x^2-x+1)^{12} ) with respect to ( x ) is:

[ \frac{d}{dx}\left[ (3x-2)^{10} \cdot (5x^2-x+1)^{12} \right] = 10(3x-2)^9 \cdot (5x^2-x+1)^{12} \cdot 3 + 12(3x-2)^{10} \cdot (5x^2-x+1)^{11} \cdot (10x - 1) ]

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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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