# How do you differentiate #V(x)=(2x^3+3)(x^4-2x)#?

Applying the rule of product

Growing, we attain

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To differentiate the function ( V(x) = (2x^3 + 3)(x^4 - 2x) ), you would use the product rule of differentiation. Here's how you apply it:

- Identify the two functions being multiplied: ( f(x) = 2x^3 + 3 ) and ( g(x) = x^4 - 2x ).
- Apply the product rule: ( V'(x) = f'(x)g(x) + f(x)g'(x) ).
- Differentiate ( f(x) ) and ( g(x) ) separately.
- Substitute the derivatives and the original functions into the product rule formula.
- Simplify the expression to get the derivative of ( V(x) ).

Here's the step-by-step process:

- ( f(x) = 2x^3 + 3 ) and ( g(x) = x^4 - 2x ).
- ( f'(x) = 6x^2 ) and ( g'(x) = 4x^3 - 2 ).
- Product rule: ( V'(x) = (6x^2)(x^4 - 2x) + (2x^3 + 3)(4x^3 - 2) ).
- Expand and simplify: ( V'(x) = 6x^6 - 12x^3 + 8x^6 - 4x^3 + 12x^3 - 6 ).
- Combine like terms: ( V'(x) = 14x^6 - 16x^3 - 6 ).

So, the derivative of ( V(x) ) is ( V'(x) = 14x^6 - 16x^3 - 6 ).

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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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