Derivatives Test (Spring 2003) MATH 131
We compute the derivative and do not simplify:
d
dx 5x6−4x−2+ 3x3/2−2= 30x5+ 8x−3+ 33
2x1/2
(1)
d
dx (sec(x)) = sec(x)·tan(x)(2)
d
dx
cos(x)
x3+ex=(−sin x)(x3+ex)−(cos x)(3x2+ex)
(x3+ex)2
(3)
d
dx ((5x2+ 2x+ 3) ·ex) = (10x+ 2) ·ex+ (5x2+ 2x+ 3) ·ex
(4)
d
dx (esin(x)) = esin(x)cos(x)(5)
d
dx (tan(ex)) = sec2(ex)·ex
(6)
d
dx ((2x2−3x−2)·sin(x3+ 1)) =(7)
= (4x+ 6x−3)·sin(x3+ 1) + (2x2−3x−2)·(cos(x3+ 1) ·(3x2))
d
dx (4x2−2√3x+ 1)−4=−4(4x2−2√3x+ 1)−5·(8x−21
2(3x+ 1)−1/2·3)(8)
d
dx cos3(x) + ex2
−x3= 3 cos(x)·(−sin(x)) + ex2
·(2x)−3x2
(9)
d
dx sin √x2−ex = cos √x2−ex·
1
2(x2−ex)−1/2·(2x−ex)(10)