Answer to Question #304844 in Calculus for jin

Question

Find the first derivative of y with respect to x. Use the given relation in its

implicit form.

a. x² + y² = a²

b. X² + 4y² = 4ay

Answer 1

$a. x^2 +y^2=a^2\\ 2x+2yy'=0\\ y'=-\frac{2x}{2y}\\ y'=-\frac{x}{y}\\ b. x^2 +4y^2=4ay\\ 2x+8yy'=4ay'\\ 4ay'-8yy'=2x\\ y'(4a-8y)=2x\\ y'=\frac{2x}{4a-8y}\\ y'=\frac{x}{2a-4y}\\$