Differentiate relations and find tangent gradients.
Example 1
For x2+y2=117, find dxdy at (6,9).
Move the mint point along the same circle. Gold marks the given point. Both axes use the same scale.Show worked answer
Answer: 9−6
- Differentiate with respect to x:2x+2y(dxdy)=0.
- Thus dxdy=y−x=9−6.
Example 2
For xy=72, find dxdy at (9,8).
The two branches remain separate at x = 0. Gold marks the given point; move the mint point on its branch. Equal axis scales.Show worked answer
Answer: 9−8
- By the product rule, y+x(dxdy)=0.
- Thus dxdy=x−y=9−8.
Example 3
For x2+y2=157, find dxdy at (11,6).
Move the mint point along the same circle. Gold marks the given point. Both axes use the same scale.Show worked answer
Answer: 6−11
- Differentiate with respect to x:2x+2y(dxdy)=0.
- Thus dxdy=y−x=6−11.