"
(a) f(x) = x3 (b) f(x) = cos x (c) f(x) = x
3
(d) f(x) = sin 5x (e) f(x) = ln x (f) f(x) =
x2
"
"
4
x3 3x4 7 3 2 2
3
3 2 "
(a) 5x15 - x7 + 3x - 2 (b) - + 3x + 7 (c) 3 x - x3 + x3 (d)
3
3 2 3 x x
3
(e) 2x - ln x + log x (f) 20x3 + log3 x - 7ex - + 5 x (g) 2 x + Ä„ (h) sin x - cos x
x2
(i) ln(2x) (j) arcsin x + arccos x
ex
(a) 3ex cos x (b) x4(x2 + 1) (c) sin 2x (d) ln (e) (x2 + 2x - x3) cos x
x
(f) ex2x (g) cos2 x (h) ln2 x (i) e2x (j) e3x
log x
2x x 1-3x2 4x5-2
"
(a) x (b) x (c) (d) (e) (f) (g)
"
3x x2+1 x3+2x-1 log3 x
2+ 3
"
x 1+ x
x ln x cos x
"
(h) (i) (j) (k) e-x (l) (m)
x2+1 1+2 x sin x+cos x x 1-sin x
"
"
4
(a) ln3 x (b) ln(1 + x2) (c) x2 + 3x (d) cos x (e) arcsin(sin x)
3
(f) ( x) (g) e3x +2x (h) eln x (i) ln ex (j) sin(x2)
"
2
1
(k) sin(e3x +6x) (l) ( + 4)4 (m) x (n) ln(ln x) (o) ln(ln(ln x))
x
2
1
(p) ln( ) (q) logx sin x (r) ecos x (s) 717x+12 ln x (t) ln(e2x + ex + e)
x
"
x
x
(u) log3(sin x · x) (v) sin(cos(4x3 + 3)) (w) 2ln(cos x) (x) arccos( ) (y) x
2 2
"
x2-3x+2 1-x
(z) logx(ln x) ( ) ( ) cos(cos(cos x)) ( ) ( ) -x
x2-7x+12 1+x
1
( ) e-2x sin 3x ( ) ( )
1+x2
f(x)g(x)
"
x
x
(a) xx (b) xx (c) x5x (d) (sin x)cos x (e) sin(x x) (f) (x2 + x)
x 2
(g) (cos x) x (h) ex (i) xsin x (j) (ln x)x (k) xx (l) (ln x)ln x
(a) 2x5 + 6x4 - 7x3 + 12x (b) ex sin(3x) (c) (2x) (d) (1 - 4x2)100
1-cos x
(a) (b) sin(1 - 2x) (c) log(x - 1)
sin x
n (a) ex (b) 2x (c) xn (d) sin x (e) sin x cos x
(a) ( ??? ) = 2x + 1 (b) ( ??? ) = - sin x (c) ( ??? ) = sin x
(d) ( ??? ) = x (e) ( ??? ) = ex (f) ( ??? ) = ex
-2
(g) ( ??? ) = ex (h) ( ??? ) = (i) ( ??? ) = - x
1+x2
Å„Å‚
òÅ‚
x2 + 2x x < 0
x0 = 0 (a) f(x) = |x| (b) f(x) =
ół
4x x e" 0
a b
Å„Å‚ Å„Å‚
òÅ‚ òÅ‚
x2 x d" 3 2x2 - ax x < 1
(a) f(x) = (b) f(x) =
"
ół ół
ax + b x > 3 x + bx x e" 1
"
(a) f(x) = log 5x (b) f(x) = log(log x) (c) f(x) = -x sin x
1
y = xe- x
x3y - xy + y = 0
f (x) = -2 f(x) = sin2 4x
f (x) e" f (x) f(x) = x3 - 9x
x+1
lim x2 · ( )
x-1
x"
sinh x, cosh x, tanh x, coth x