Derivative Worksheet - Calculus
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1
2Differentiation worksheet #1 for Calculus 1
Use the limit definition of derivative to differentiate the following functions:
(1) x + 1
(4)
x
4
x
(2) 2/x
(5)
(without simplifying first!)
x + 1
2
(3) x
+ x
Here is a list of differentiation rules:
A. Power Rule
B. Chain Rule
C. Product Rule D. Quotient Rule
For each given function, mark which differentiation rule you would apply
.
x
3 2
(6) x
(11)
1
x
2
4
(7) x
x
1 2
1 3
πx
(12) (x + x
)(cos(x) + x
)
(8)
4
(13) cos
(x)
6
2
4
4
(9) x
x
+ 1
(14) cos(x
)
2 sin(x)
4
(10) cos(x
)
(15) x
You are given the following information: f and g are continuous differentiable functions such that f (5) = 3,
g(5) = 4, f (5) = 7, g (5) =
2. Find h(5) and h (5) for each of the following functions h:
(16) h = f + g
(20) h =
f + f
g
2
f
+ g
(17) h = f
g
(21) h =
(18) h = 2f /g
f + g
2
(19) h = g
3g
Find the derivative. Show every time you use one of the rules A–D above.
3
Example. To find the derivative of x
+ sin(x):
d
d
d
3
3
(x
+ sin(x)) =
(x
) +
(sin(x))
dx
dx
dx
2
= 3x
+ cos(x)
A. power rule
πx
3 2
(22) x
(30)
6
1
5
4 3
1 3
(23) x
+ 2x
+
x
4
(31) x
πx
2+1
(24)
x
7
1
(32) x
7x
(25)
5
3
4 7
2
(33)
x
+ 3x
(26) 5/x
4
(27) 25
5
(34) x
+
5x
3
(28)
x +
x
3
4
2
(35) ax
+ bx + c, where a, b, c are constants
0 4
(29) 1/x
(36) 5 cos(x)
2 cos(x)
1
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