Calculus- Early Transcendentals, 2021a

573
4.5.18 −3(4 − x) 2
4.5.19 6x(x 2 + 5) 2
4.5.20 −12x(6 − 2x 2 ) 2
4.5.21 24x 2 (1 − 4x 3 ) −3
4.5.22 5 + 5/x 2
4.5.23 −8(4x − 1)(2x 2 − x + 3) −3
4.5.24 1/(x + 1) 2
4.5.25 3(8x − 2)/(4x 2 − 2x + 1) 2
4.5.26 −3x 2 + 5x − 1
4.5.27 6x(2x − 4) 3 + 6(3x 2 + 1)(2x − 4) 2
4.5.28 −2/(x − 1) 2
4.5.29 4x/(x 2 + 1) 2
4.5.30 (x 2 − 6x + 7)/(x − 3) 2
4.5.31 −5/(3x − 4) 2
4.5.32 60x 4 + 72x 3 + 18x 2 + 18x − 6
4.5.33 (5 − 4x)/((2x + 1) 2 (x − 3) 2 )
4.5.34 1/(2(2 + 3x) 2 )
4.5.35 56x 6 + 72x 5 + 110x 4 + 100x 3 + 60x 2 + 28x + 6
4.5.36 y = 23x/96 − 29/96
4.5.37 y = 3 − 2x/3
4.5.38 y = 13x/2 − 23/2
4.5.39 y = 2x − 11
4.5.40 y = 20 + 2√ 5
5 √ 4 + √ 5 x + 3√ 5
5 √ 4 + √ 5
4.5.41 ( f (g(1))) ′ = 20
4.5.42 g ′ (x)=2x( f (x 2 )+x 2 f ′ (x 2 ))
4.6.1 2ln(3)x3 x2
4.6.2
4.6.3 2e 2x
cosx − sinx
e x
4.6.4 e x cos(e x )
4.6.5 cos(x)e sinx
(
4.6.6 x sinx cosxlnx + sinx )
x
4.6.7 3x 2 e x + x 3 e x
4.6.8 1 + 2 x ln(2)
4.6.9 −2xln(3)(1/3) x2
4.6.10 e 4x (4x − 1)/x 2
4.6.11 (3x 2 + 3)/(x 3 + 3x)
4.6.12 −tan(x)
4.6.13 (1 − ln(x 2 ))/(x 2 √ln(x 2 ))
4.6.14 sec(x)
4.6.15 x cos(x) (cos(x)/x − cos(x)ln(x))
4.6.19 e
4.7.1 1. x/y
2. −(2x + y)/(x + 2y)
3. (2xy − 3x 2 − y 2 )/(2xy − 3y 2 − x 2 )
4. sin(x)sin(y)/(cos(x)cos(y))
5. − √ y/ √ x
6. (ysec 2 (x/y) − y 2 )/(xsec 2 (x/y)+y 2 )
7. (y − cos(x + y))/(cos(x + y) − x)
8. −y 2 /x 2
4.7.2 1
4.7.3 y = 2x ± 6
4.7.4 y = x/2 ± 3