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

• sbose27
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.
sbose27
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.

It's a simple extension of the product rule: (uvw)' = u'vw + uv'w + uvw', where u,v and w are functions of x.

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

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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