Question #304844

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


1
Expert's answer
2022-03-02T17:02:16-0500

a.x2+y2=a22x+2yy=0y=2x2yy=xyb.x2+4y2=4ay2x+8yy=4ay4ay8yy=2xy(4a8y)=2xy=2x4a8yy=x2a4ya. 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}\\


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