Look for factors that are common to both terms.cataschok said:Homework Statement
use product rule to find the derivative of g(x)=(2x+1)^2(x-7)^3
Homework Equations
i've applied chain rule and product rule to get...
The Attempt at a Solution
4(2x+1)(x-7)^3+3(2x+1)^2(x-7)^2
i need to factor out to get the following..
5(x-7)^2(2x-5)(2x+1)
That's the final answer from the book. But the steps to get there... I'm lost. Can anyone help me out on getting it to the factored form?
The factored form of a derivative is a polynomial expression that represents the derivative of a given function. It is written in the form of (x-a)^n, where a is the root of the function and n is the degree of the root.
The factored form of a derivative allows us to easily identify the critical points and inflection points of a function. It also helps us to graph the function and determine its behavior at specific points.
To find the factored form of a derivative, you need to take the derivative of the given function and then factor out any common factors. Next, determine the roots of the function and write the derivative in the form of (x-a)^n.
No, the factored form of a derivative only gives us information about the slope of a function at a specific point. It cannot be used to find the original function as it does not provide information about the constant term or the initial conditions.
The factored form of a derivative is written in the form of (x-a)^n, while the expanded form is written as a polynomial expression. The factored form is useful for identifying critical and inflection points, while the expanded form is better for evaluating the derivative at a specific point.