# How do you use the chain rule to differentiate #y=(x^2+3)^4#?

Chain rule is:

We have:

We multiply these two results to get the final solution:

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The chain rule states that,

Multiply these results together to get,

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To differentiate ( y = (x^2 + 3)^4 ) using the chain rule, you first find the derivative of the outer function (in this case, ( u^4 )) with respect to ( u ), and then multiply it by the derivative of the inner function (in this case, ( x^2 + 3 )) with respect to ( x ). The derivative of ( u^4 ) is ( 4u^3 ), and the derivative of ( x^2 + 3 ) is ( 2x ). Therefore, the derivative of ( y ) with respect to ( x ) is ( 4(x^2 + 3)^3 \cdot 2x ).

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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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