# How do you use the Product Rule to find the derivative of #3x(2x-1)^3#?

This will allow you to use the formula

In your case, you have

This means that you can write

Your target derivative will thus be

This can be further simplified to

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To use the Product Rule to find the derivative of (3x(2x-1)^3), you first identify the two functions being multiplied: (f(x) = 3x) and (g(x) = (2x - 1)^3). Then, apply the Product Rule, 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 the Product Rule, the derivative of (3x(2x-1)^3) is:

[f'(x) = f(x) \cdot g'(x) + g(x) \cdot f'(x)]

[= 3x \cdot 3(2x - 1)^2 \cdot 2 + (2x - 1)^3 \cdot 3]

[= 6(2x - 1)^2 + 3(2x - 1)^3]

[= 6(2x - 1)^2 + 3(2x - 1)^3]

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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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