Engineering Board Exam Reviewer · Implicit Differentiation · medium

Find dy/dx if x3+y3=6xy.

1. x2 - 2 y- 2 x + y2
2. - x2 + 2 y- 2 x + y2
3. - x2 + 2 y2 x + y2
4. 2 - x2y2

Answer

B. - x2 + 2 y- 2 x + y2

Solution

Differentiate: 3x2+3y2y'=6y+6xy'. Collect y': y'(3y2-6x)=6y-3x2, so dy/dx=2y-x2/y2-2x.

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2. Find dy/dx if xy=yx (for x,y>0).
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4. Find dy/dx if (x+y)=y.
5. Find dy/dx if x2-xy+y2=7.
6. Find dy/dx at the point (0,1) on the curve exy+x=y.
7. Find the slope of the curve x2y+xy2=6 at the point (1,2).

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