Science:Math Exam Resources/Courses/MATH100/December 2019/Question 2 (b)
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q8 • Q9(a) • Q9(b) • Q12 • Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 • Q6 • Q7 •
Question 2 (b) 

Find at the point (x,y)=(1,0) if . 
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 

Whenever there is a variable as an exponent, take the natural logarithm followed by the exponential. In the case at hand . 
Hint 2 

Treating y as a function of x, take the derivative w.r.t. to x of both sides of the equation. As a result of the chain rule there will be some y' terms on both sides. Solve for them after evaluating at (x,y)=(1,0). 
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 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Whenever there is a variable as an exponent, take the natural logarithm followed by the exponential. In the case at hand . Treating y as a function of x, the derivative w.r.t. to x of the LHS of the equation must be the same as that one of the RHS:
While the right hand side is
Therefore,
If the question asked for as a function of x we would just solve for y' in the previous equation. However, since they are asking for the value of this function at (x,y)=(1,0), it's faster to evaluate directly in this expression and then solve for y'(x=1). Indeed, substituting these values above results in:
Which yields 