MTH 124
FS15 Derivative Worksheet
Name:
The purpose of this worksheet is to provide an opportunity to practice differentiation
formulas. It will not be graded and you are not expected to finish in class.
Exercises
(1) f (x) = x2 + 2x + 1
(14) t(x) = ln(x2 + 3x)ex
(2) g(x) = 3xex
(15) n(x) =
(3) h(x) = ln(x2 + x)
(16) a(t) = t(t3 + t + et )
(4) t(x) = 3x3 e7
(17) f (u) =
(5) n(x) =
x+1
x−1
(18) g(x) =
2 −x
1
ln x+x
e7 +ln 2+1
u
√
−1
x3 + 2x + 1
2
(6) a(t) = tet
(7) f (u) =
u2
ln(1+eu )
(8) g(x) = e
(9) h(y) =
(10) s(t) =
(19) h(y) = e5y + ln(2y) +
√
4
3x4 +3x2 +1
1
(7y)2
(5x3 +2x2 +2) ln(x)
e3x +x
(20) s(t) =
15
y
t3 +7t+1
t
(21) f (x) = ln(ex (x2 + 1))
(22) g(x) = e(x
2 +3)7 (x−1)5
(23) h(x) = ln x − ln( x1 )
√
(11) f (x) = (x2 + x)100
(24) t(x) = y(2x −
(12) g(x) = (3x2 + x + 1)ex ln x
(25) n(x) = (x + 1)4 (x − 1)4 x3
(13) h(x) =
(x2 +x+1)(4x )
x ln x
2
(26) a(t) ett2−1
−1
5)
2
u4
ln(1+eu )
(29) h(y) = |y 2 |
q
(30) s(t) =
(27) f (u) =
(28) g(x) =
x2 +x
ln x+1
formulas
(1)
d
c
dx
(2)
d n
x
dx
= nxn−1
(3)
d x
e
dx
= ex
(4)
d x
a
dx
= ax ln(a)
(5)
d
dx
(6)
d
[cf (x)]
dx
(7)
d
[(f (x)
dx
(8)
d
[(f (x)g(x)]
dx
(9)
d f (x)
[
]
dx g(x)
(10)
=0
ln(x) =
d
[f
dx
1
x
= cf 0 (x)
± g(x)] = f 0 (x) ± g 0 (x)
=
= f 0 (x)g(x) + f (x)g 0 (x)
f 0 (x)g(x)−f (x)g 0 (x)
(g(x))2
◦ g(x)] =
d
f (g(x)]
dx
= f 0 (g(x))g 0 (x)
1
|t|