# How do you differentiate #f(x)=(x-5)^3-x^2+5x# using the sum rule?

The sum rule is simple. All we have to do is find the derivative of each part of the sum and add them back to one another.

I've written the rules we'll need to continue in finding the derivatives.

Through the Chain Rule:

We can add all these back together:

And, simplify:

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To differentiate the given function ( f(x) = (x - 5)^3 - x^2 + 5x ) using the sum rule, differentiate each term separately and then add them together. The sum rule states that the derivative of a sum is the sum of the derivatives of the individual terms.

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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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