# How do you differentiate #f(x)=(x-3)^2+(x-4)^3# using the sum rule?

You can apply the sum rule right away to the two expressions added.

You can then differentiate each part using the chain rule.

Combining like terms, we get

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To differentiate ( f(x) = (x - 3)^2 + (x - 4)^3 ) using the sum rule, you differentiate each term separately and then add the results.

So,

[ \begin{align*} f(x) &= (x - 3)^2 + (x - 4)^3 \ f'(x) &= \frac{d}{dx}[(x - 3)^2] + \frac{d}{dx}[(x - 4)^3] \ &= 2(x - 3) + 3(x - 4)^2 \ &= 2x - 6 + 3(x - 4)^2 \end{align*} ]

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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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