Derivative Worksheet - Calculus Page 2
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1
22
5 6
(37) tan(x) + csc(x)
(51) cos(x
)
2
(38) 5 sin(x) + x
(52) tan(2πx +
)
2
1 7
(39) x
cos(x)
2
(53)
x
16
(40) sin(x) cos(x)
2
(54)
16
x
2
1
(41) (x
+
) tan(x)
3
3
(55)
x
2x + 1
(42)
x(sin(x) + cos(x))
4
(56) sin
(x)
(43) sin(x) + sin(x) cos(x)
1
(57)
1 +
x
4
(44)
2
(58)
2x + 1(x
+ 1)
2
x
+ 2
x
2
x
x + 2
(45)
(59)
x + sin(x)
2
x
x + 2
2x
x
(60) cos( x) cos(x)
(46)
3
x
2
(61) cos( x
+ 2)
x + 1
(47)
2
2
(62)
cos(x
+ 2) +
cos
(x) + 2
2
sin(x) + sin(x) cos(x)
(63) tan( 2x + 5)
(48)
2 x + 1
x
(64) sin
3 4
(49) (x + 1)
x + 1
4
(50) sin(x
)
Find an equation for the tangent line to the given function at the given point.
2
3
(65) y = 2x
+ x + 1, at (4, 37)
(68) y = x
x, at (2/3, 10/27)
3
(66) y = x
x, at (1/3, 8/27)
2
(69) y =
25
x
, at ( 4, 3)
3
(67) y = x
x, at (1/2, 3/8)
(70) y = sin(x)
, at (π, π/2)
2
Find the second derivative of each of the following functions.
4
2
(71) x
+ 2x
+ 3
(74) tan(x)
(72) sin(x) + 1
(75)
x
(73) sin(2x)
“Cruel and unusual derivatives.” These are harder; only try them if you feel all right with everything up
to this point. Find the first derivatives, showing your steps:
(76)
(79)
2
2 sin(x
) + 3 cos( x)
x +
x +
x
2
2
2 sin
(x)
5 cos
(x)
(77)
(80)
sin(x) cos(x) x
1
(78)
1
1 +
2
2
1
2
1+
sin(x
) cos(x
) x
+ 1
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