Section 4.4 Implicit Differentiation
𝑑𝑦
#1-24: Use implicit differentiation to determine 𝑑𝑥 .
1) 3x + y = 12
2) 4x2 + y = 3x – 2
3) 5x2 + 3y = 2x – 4
4) 4x3 + 7y = x2 + 5x – 3
5) 2x + 3y2 = 5x2 – 2x3
6) 5y3 + 6x2 = 4 – 3x
7) 𝑥 1⁄2 + 𝑦 1⁄3 = 3
8) 𝑥 3⁄4 + 𝑦 1⁄2 = 4
9) 2x2 + xy = 5
10) x3 + xy = 3
11) 2x2 + xy2 = 5
12) x3 + xy3 = 3
13) 2x2 + xy = 5y
14) x3 + xy = 3y
15) 2x2 + xy2 = 5y3
16) x3 + xy3 = 3y3
17) e4y + 3x = 12x2
18) 3e2y + x2 = 5x3
19) e4y + 3x = 12y2
20) 3e2y + x2 = 5y3
21) 3√𝑦 + 3𝑥𝑦 = 2𝑥 2
22) √𝑦 + 4𝑥𝑦 = 3𝑥 2
23) xey + 2y = 3x
24) x2e2y + 3y2 = 5x
#25- 34: Find the equation of the line tangent to the graph at
the indicated point.
25) x2 + y2 = 25; (4,3)
26) x3 + y3 = 9; (2,1)
27) 3x2 + 2y = 25; (3,-1)
28) 2x3 + 3y2 = 57; (3,1)
29) 2𝑦 2 − √𝑥 = 4; (16,2)
3
30) 3𝑦 3 + √𝑥 = 26; (8,2)
31) y2 + 2y =11 + 4x; (1, 3)
32) y3 - 7y = 40 – 2x; (2,4)
33) xey + 2y =3x - 4; (2,0)
34) x2e2y + 3y2 = 5x - 6 (3,0)
𝑑𝑟
#35-42: Use implicit differentiation to determine 𝑑𝑡 .
35) 𝐴 = 2𝜋𝑟
36) 𝐴 = 𝜋𝑟 2
37) 𝑉 = 5 + 6𝑟
38) 𝑉 = 2𝑟 2 + 8
39) 𝑟 = 6𝑥 − 4
40) r = 12x + 10
41) r = y2 + 3
42) r = 5y2 + 6