Calculus, MET1 2011 ADV 4d Differentiate `y=sqrt(9-x^2)` with respect to `x`. (2 marks) --- 4 WORK AREA LINES (style=lined) --- Show Answers Only `- x/sqrt(9-x^2)` `-6 sqrt(9-x^2) + c` Show Worked SolutionIMPORTANT: Some students might find calculations easier by rewriting the equation as `y=(9-x^2)^(1/2)`. a. `y` `= sqrt(9-x^2)` `= (9-x^2)^(1/2)` `text{Using the function of a function rule (or “chain” rule)}` `dy/dx` `=1/2 xx (9-x^2)^(-1/2) xx d/dx (9-x^2)` `= 1/2 xx (9-x^2)^(-1/2) xx -2x` `=-x/sqrt(9-x^2)` b. `int (6x)/sqrt(9-x^2)\ dx` `= -6 int (-x)/sqrt(9-x^2)\ dx` `= -6 sqrt(9-x^2) + c`