60
9.34
9.39
9.41
9.42
9.40
In Problems 9.35-9.44, use the chain rule (and possibly other rules) to find the derivative of the given function.
Let g(x) = x2-4 and /(*) = !/*. Then (f°g)(x)=f(g(x))=f(x2 - 4) = l/(x2 - 4).
9.35
9.36
9.37
9.38
(7 + 3x)
s
.
D x [(l + 3x)
5 ] = 5(7 + 3x)
4 • D f (l + 3x) = 5(7 + 3*)" • (3) = 15(7 + 3x)
4
.
(2x-3)2 .
Dx[(2x - 3)-2] = (-2)(2* - 3)-3 • Dx(2x - 3) = -2(2x - 3)-3 • (2) = -4(2* - 3)~3.
(3jc
2 + 5)3
.
D t [(3x
2 + 5)3 ] = (-3)(3x
2 + 5)4 • D,(3x
2 + 5) = -3(3x
2 + 5)"
4 • (6x) = -I8x(3x
2 + 5)'
4
.
CHAPTER 9
= 4D,[(3*
2 -x + 5)'
1 ] = 4(-l)(3x
2 -x + 5)~
2 D x (3x
2 -x + 5)
= -4(3x
2 -x + 5)~
2 (6* - 1) =
*2(1-3*3)1/3.
Dx[x2(l - 3x3)"3] = x2Dx(l - 3*3)1'3 + 2x(l - 3*3)1'3 = X(\)(1 - 3*3)-2'3 • D(\ - 3*3) + 2x(l ~ 3x3)113
= \x\\ - 3^3)-2'3 • (-9x2) + 2x(l - 3x3)1/3 = -3*4(1 - 3x3)"2'3 + 2*(1 - 3;c3)"3
= x(l - 3^3)-2/3[-3A:3 + 2(1 - 3*3)] = x(\ - 3x3)-2/3(2 - 9*3) =
(7x3-4x2 + 2)1/4.
D^Tjc3 - 4;c2 + 2)1'4 = K7*3 - 4^2 + 2)'3'4 • D,(7x3 - 4^2 + 2) = U7*3 - 4x2 + 2)~3/4(2U2 - 8x)