Exploring T9 Q11d Implicit Differentiations Sm015

Exploring T9 Q11d Implicit Differentiations Sm015 reveals several interesting facts.

  • If xy=2(x-y)^2 find the following values at the point (1, 2). (a) dy/dx (b) d^2/dx^2.
  • A curve with an equation x^2+y^2+ay=b where a and b are constant. (a) Find dy/dx. (b) If the slope at point (1,3) is -1/2, find a and ...
  • Given x^2+y^2=5x+5y. Find y'' at (5,0).
  • Given x^2+y^2=2y, find dy/dx. Show that d2y/dx2=1/(1-y)^3. Hence, express in term of y for 2/x(dy/dx)^3-x^2d2y/dx2.
  • Find dy/dx for lny=2y^2-x at the point (2, 1).

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