How do you use the chain rule to differentiate #f(x)=sqrt(4x^3+6x)#?
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To differentiate f(x) = sqrt(4x^3 + 6x) using the chain rule, follow these steps:

Identify the outer function and the inner function.
 Outer function: sqrt(u), where u = 4x^3 + 6x
 Inner function: u = 4x^3 + 6x

Calculate the derivative of the outer function with respect to its argument (u) and the derivative of the inner function with respect to x.

Apply the chain rule formula: d/dx[sqrt(u)] = (1/2) * (u)^(1/2) * du/dx.

Substitute u = 4x^3 + 6x and du/dx = d/dx[4x^3 + 6x] into the chain rule formula to find the derivative of f(x).
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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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