Science:Math Exam Resources/Courses/MATH104/December 2014/Question 01 (k)
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Question 01 (k) 

Find , where Note that refers to the inverse tangent function, which is also denoted by arctan. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

If you remember the derivative of you can just use that directly. Don't forget the chain rule! Otherwise, take the tangent of both sides and then compare the derivatives. Again, don't forget the chain rule! 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

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Please rate my easiness! It's quick and helps everyone guide their studies. The formula for derivative of . Therefore, using the chain rule, we obtain that . Plugging in we find that the final answer is

Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. We can also solve this without using the derivative of directly. Instead, let's taking the tangent of both sides yields Comparing the derivatives  remember the chain rule  we see that Finally, we plug in and use that to obtain the final answer 