Science:Math Exam Resources/Courses/MATH100 A/December 2023/Question 06
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 • Q7 • Q8 • Q9 • Q10 • Q11 • Q12 • Q13 • Q14 • Q15 • Q16 • Q17 • Q18 • Q19 • Q20 • Q21 • Q22 • Q23 • Q24 • Q25 • Q26 • Q27(a) • Q27(b) • Q27(c) • Q28(a) • Q28(b) • Q29(a) • Q29(b) • Q30 •
Question 06 

Let . Find . 
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 

Do you know of a function that you could apply to that would simplify the expression so there is no longer a variable in the exponent? 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. None of the usual derivative rules we know will help with this function, so we will need to transform it into a form that we can use derivative rules with! The issue is the variable in the exponent and the base, so if we apply the logarithm to both sides of the expression, we can bring the variable in the exponent down: Note: we need to make sure , otherwise will be undefined. Luckily, we are interested in the domain where , and does not equal zero over this domain. Now, use implicit differentiation: Sub in : . 