Derivative of (x+3)(x-4)(x+5): A Simple Guide

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In summary, The derivative of 3 groups of parentheses (x+3)(x-4)(x+5) is (x+3)(x-4) + (x+3)(x+5) + (x-4)(x+5) = 3x^2-2x-7.
  • #1
sbose27
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Sorry for not using JavaScript or whatever script is needed, I don't have enough time to figure it out b/c my class is soon... anyways I just need to know know to find the derivative of 3 groups of parentheses

(x+3)(x-4)(x+5)

I've tried using the product rule on the first two and then using the rule on the result from that and (x+5) but it's not working. I'm an idiot.. thanks for any help.
 
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It's a simple extension of the product rule: (uvw)' = u'vw + uv'w + uvw', where u,v and w are functions of x.
 
  • #3
neutrino said:
It's a simple extension of the product rule: (uvw)' = u'vw + uv'w + uvw', where u,v and w are functions of x.

okay thanks a lot
 
  • #4
sbose27 said:
I've tried using the product rule on the first two and then using the rule on the result from that and (x+5) but it's not working.

That should work actually.
If you call the 3 functions u(x), v(x) and w(x) and let y(x) = u(x)v(x), then [y(x)w(x)]' = y'w + yw'. Just replace y = uv and y' = u'v + uv', you get (u'v + uv')w + uvw' = u'vw + uv'w + uvw', which is exactly what neutrino.
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It can be thought of as the slope of a line tangent to the curve of the function at that point.

Why do we use derivatives?

Derivatives are used in many areas of science and mathematics, including physics, economics, and engineering. They help us understand how a system or function is changing over time, and can be used to optimize processes or make predictions.

What is the difference between a derivative and an integral?

While derivatives represent the rate of change of a function, integrals represent the accumulation of a function over a certain interval. In other words, derivatives tell us how a function is changing, while integrals tell us the total amount of change over a given interval.

How do you find the derivative of a function?

The most common method for finding the derivative of a function is using the rules of differentiation, such as the power rule or product rule. These rules involve taking the limit of a function as the change in the input variable approaches 0.

Can derivatives be negative?

Yes, derivatives can be negative. A negative derivative indicates that the function is decreasing at that point, while a positive derivative indicates that the function is increasing at that point.

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