# What is the derivative of #(1+4x)^5(3+x-x^2)^8#?

You can differentiate this function by using the chain rule and the product rule.

Notice that your function can be written as

which means that its derivative can be determined using the product rule

This will get you

For #g(x) you have

This will get you

Take these derivatives to your target calculation to get

This is equivalent to

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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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