What is the mistake in solving this derivative?

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In summary, a derivative is a mathematical concept used to find the rate of change of a function at a specific point. It is important to solve derivatives because they help us understand complex systems and make predictions. There are various methods for solving derivatives, such as the power rule and the chain rule. Common mistakes when solving derivatives include forgetting to apply the chain rule and mixing up different rules. To improve your skills in solving derivatives, it is recommended to practice with different functions and seek help from resources like tutors or online tutorials.
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bk1
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Hi everyone,

I'm having trouble solving this one. I just don't really see what I'm doing wrong.

Homework Statement


X² - x - 2
X² + 5x + 6


Homework Equations





The Attempt at a Solution


(( x-1 ) * x² + 5x + 6 ) - (( x + 5 ) * x²-x-2 )
( x² + 5x + 6)²

So 8x² -6x-16
(x² + 5x + 6)²

Now I know this isn't the correct awnser. Because it should say
6x² + 16x + 4
( x² + 5x+6)²

Could anyone point out to me what I'm doing wrong?
Thanks in advance.
Tim
 
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  • #2


The derivative of x^2 is 2x, not x.
 

What is a derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is often used to find the slope of a curve or the instantaneous rate of change at a particular point.

Why is it important to solve derivatives?

Derivatives are important because they can help us understand the behavior of a function or a system. They are used in many fields such as physics, economics, and engineering to analyze and make predictions about the behavior of complex systems.

What are the different methods for solving derivatives?

There are several methods for solving derivatives, including the power rule, product rule, quotient rule, and chain rule. Each method is used to find the derivative of a specific type of function.

What are some common mistakes when solving derivatives?

Common mistakes when solving derivatives include forgetting to apply the chain rule, mixing up the power rule with the product or quotient rule, and not simplifying the final answer. It is important to carefully follow the rules and double check your work to avoid these mistakes.

How can I improve my skills in solving derivatives?

The best way to improve your skills in solving derivatives is through practice. Choose a variety of functions and try to find their derivatives using different methods. You can also seek help from a tutor or an online resource to learn new techniques and get feedback on your work.

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