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
a.x2+y2=a22x+2yy′=0y′=−2x2yy′=−xyb.x2+4y2=4ay2x+8yy′=4ay′4ay′−8yy′=2xy′(4a−8y)=2xy′=2x4a−8yy′=x2a−4ya. 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}\\a.x2+y2=a22x+2yy′=0y′=−2y2xy′=−yxb.x2+4y2=4ay2x+8yy′=4ay′4ay′−8yy′=2xy′(4a−8y)=2xy′=4a−8y2xy′=2a−4yx
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