Science:Math Exam Resources/Courses/MATH104/December 2012/Question 01 (c)
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Question 01 (c) 

Differentiate the function 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Notice that both the base and exponent of are functions of , so neither the power rule nor the exponential derivative rule will work here. What operation can you do to to express it as a product of functions? 
Hint 2 

Start by taking the logarithm of ƒ. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Use logarithmic differentiation on this function. Taking the derivative of this equation with respect to gives: 