Simplifying and Rearranging Polynomial Expressions

In summary, the product rule is a formula used in calculus to find the derivative of a product of two functions. It involves taking the derivative of each function separately and then combining them using the product rule formula. The product rule is important because it simplifies the process of finding derivatives of products and can be extended to more than two functions. Common mistakes when using the product rule include not distributing the derivative to both functions and mixing up the order of the functions.
  • #1
GeneralOJB
42
0
Differentiate and simplify:
y=(x+1)(2x-3)[tex]^{4}[/tex]

I got:
8(x+1)(2x-3)[tex]^{3}[/tex] + (2x-3)[tex]^{4}[/tex].

But the answers in the answer booklet say:
5(2x+1)(2x-3)[tex]^{3}[/tex]

I put both answers in Wolfram Alpha and found they were both equal. So this is just a matter of simplifying/rearranging.

Could someone please explain to me how to simplify my answer to get the answer in the booklet? This one's annoying me as I just can't seem to do it.
 
Last edited:
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  • #2
Factor out a (2x-3)3.
 
  • #3
Thanks so much! I can't believe I never thought to do that.
 

Related to Simplifying and Rearranging Polynomial Expressions

What is the product rule for differentiation?

The product rule is a formula used in calculus to find the derivative of a product of two functions. It states that the derivative of the product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.

How do you apply the product rule?

To apply the product rule, first identify the two functions that are being multiplied together. Then, take the derivative of each function separately. Finally, use the product rule formula to combine the two derivatives and simplify if possible.

Why is the product rule important?

The product rule is important because it allows us to find the derivative of a product of two functions, which is a common occurrence in calculus. Without the product rule, we would have to use more complex methods to find the derivative of a product.

What are the common mistakes when using the product rule?

One common mistake when using the product rule is forgetting to distribute the derivative to both functions in the product. Another mistake is mixing up the order of the functions in the product when applying the product rule formula.

Can the product rule be extended to more than two functions?

Yes, the product rule can be extended to more than two functions. For three functions, the formula becomes the first function times the derivative of the second function, plus the second function times the derivative of the first function, plus the third function times the derivative of the first two functions. This pattern can be continued for any number of functions.

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