Is this correct?Yes, your solution is correct. Good job!

  • Thread starter BuBbLeS01
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    Derivative
In summary, the derivative of 2sinxcosx is 2cos(2x) or sin(2x). This can be simplified by using trig identities.
  • #1
BuBbLeS01
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1 more derivative problem!

Homework Statement


Find the derivative of...
2sinxcosx
not simplified

The Attempt at a Solution


(2cosxcosx) - (2sinxsinx)

I just want to make sure this is right
 
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  • #2
yes that is correct..but you should simplify cosxcosx to [tex]cos^2x[/tex] and likewise with the sinxsinx
 
  • #3
rock.freak667 said:
yes that is correct..but you should simplify cosxcosx to [tex]cos^2x[/tex] and likewise with the sinxsinx

And, when you're done, does that result look like a trig identity you've seen before? Could you have gotten the same result by using a trig identity on 2 sin x cos x first?
 
  • #4


dy/dx = 2 sin x . -sin x +cos x . cos x= 2 ( cos squared - sin squared)

So yes your correct
 
Last edited:
  • #5


Which, as dynamicsolo hinted, is the same as 2 cos(2x) and could have been done more simply by recognizing that 2 sin(x) cos(x)= sin(2x).
 

1. What is a derivative problem?

A derivative problem involves finding the rate of change of a function at a given point. It is an important concept in calculus and is used to solve a variety of real-world problems.

2. How do I solve a derivative problem?

To solve a derivative problem, you must first find the derivative of the given function. This can be done by using the power rule, product rule, chain rule, or quotient rule. Once you have the derivative, you can plug in the given point to find the rate of change at that specific point.

3. What are the applications of derivative problems?

Derivative problems have many applications in fields such as physics, engineering, economics, and more. They are used to find maximum and minimum values, optimize functions, and analyze rates of change in various systems.

4. Can I use a calculator to solve derivative problems?

Yes, there are several online calculators and software programs that can help you solve derivative problems. However, it is important to understand the concepts and steps involved in solving these problems, rather than relying solely on a calculator.

5. What are some common mistakes to avoid when solving derivative problems?

Some common mistakes to avoid when solving derivative problems include mixing up the rules, forgetting to include the chain rule, and making careless errors in calculations. It is important to double-check your work and practice regularly to avoid these mistakes.

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