1
Implicit Differentiation- HW Problems
𝑑𝑦
Find .
𝑑𝑥
1. 4𝑥 2 + 16𝑦 2 = 1
2. 𝑥 2 + 𝑥𝑦 + 𝑦 2 = 3
3. 𝑥 2 𝑦 − 𝑥𝑦 2 = 2
4. cos(𝑥 − 𝑦) = 𝑦 2 sin(𝑥 )
𝑦
5. tan ( ) = 𝑥 2 + 𝑦 2
𝑥
1
6. 𝑦 = (𝑥 − cos(𝑥 )) 3
1
7. 𝑦 = (𝑥 − cos(𝑦)) 3
Find an equation of the tangent line at the given point.
𝜋
8. 𝑥𝑠𝑖𝑛(𝑦) = 1 𝑎𝑡 (2, )
6
𝜋 𝜋
9. 𝑦𝑠𝑖𝑛(8𝑥 ) = 𝑥𝑐𝑜𝑠(2𝑦) 𝑎𝑡 ( , )
2 4
10. 𝑥 2 + 𝑥𝑦 − 𝑦 2 + 𝑦 = 1 𝑎𝑡 (1,2)
Implicit Differentiation- HW Problems
𝑑𝑦
Find .
𝑑𝑥
1. 4𝑥 2 + 16𝑦 2 = 1
2. 𝑥 2 + 𝑥𝑦 + 𝑦 2 = 3
3. 𝑥 2 𝑦 − 𝑥𝑦 2 = 2
4. cos(𝑥 − 𝑦) = 𝑦 2 sin(𝑥 )
𝑦
5. tan ( ) = 𝑥 2 + 𝑦 2
𝑥
1
6. 𝑦 = (𝑥 − cos(𝑥 )) 3
1
7. 𝑦 = (𝑥 − cos(𝑦)) 3
Find an equation of the tangent line at the given point.
𝜋
8. 𝑥𝑠𝑖𝑛(𝑦) = 1 𝑎𝑡 (2, )
6
𝜋 𝜋
9. 𝑦𝑠𝑖𝑛(8𝑥 ) = 𝑥𝑐𝑜𝑠(2𝑦) 𝑎𝑡 ( , )
2 4
10. 𝑥 2 + 𝑥𝑦 − 𝑦 2 + 𝑦 = 1 𝑎𝑡 (1,2)
