What is the second derivative of #f(x)= 2x^3 sqrt(4x^2)#?
Applying product rule,
Simplifying,
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To find the second derivative of ( f(x) = 2x^3  \sqrt{4  x^2} ), follow these steps:

Find the first derivative ( f'(x) ).

Find the second derivative ( f''(x) ).

First derivative: [ f'(x) = 6x^2 + \frac{x}{\sqrt{4x^2}} ]

Second derivative: [ f''(x) = 12x  \frac{3x^2}{(4x^2)^\frac{3}{2}} ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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