What is the second derivative of? : #2(x^21)^3#
To find the second derivative, you need to find the first derivative, so let's do that immediately:
I used the chain rule and product rule to find the first derivative. Now let's find the second derivative:
#d/dx 12x(x^21)^2 = 12(x^21)^2+12x*[2(x^21)*2x] = 12(x^21)^2 + 48x^2(x^21)#
For the second derivative, I used the product rule and chain rule.
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# (d^2)/(dx^2) 2(x^21)^3 = 12(x^21)(5x^21) #
First we generate the first derivative using the chain rule:
Then, we generate the second derivative using the product rule and the chain rule:
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To find the second derivative of (2(x^2  1)^3), follow these steps:

Find the first derivative using the chain rule: [f'(x) = 6(x^2  1)^2 \cdot 2x]

Simplify the first derivative: [f'(x) = 12x(x^2  1)^2]

Now, differentiate the first derivative to find the second derivative: [f''(x) = 12(x^2  1)^2 + 24x^2(x^2  1)]

Simplify the second derivative: [f''(x) = 12(x^2  1)^2 + 24x^2(x^2  1)]
Therefore, the second derivative of (2(x^2  1)^3) is (12(x^2  1)^2 + 24x^2(x^2  1)).
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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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