Calculus/Differentiation/Basics of Differentiation/Exercises
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Find the Derivative by Definition[edit]
Find the derivative of the following functions using the limit definition of the derivative.
1.
2.
3.
4.
5.
6.
7.
8.
9.
Prove the Constant Rule[edit]
10. Use the definition of the derivative to prove that for any fixed real number ,
Find the Derivative by Rules[edit]
Find the derivative of the following functions:
Power Rule[edit]
11.
12.
13.
14.
15.
16.
17.
18.
19.
Product Rule[edit]
20.
21.
22.
23.
24.
25.
26.
27.
28.
Quotient Rule[edit]
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
Chain Rule[edit]
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
Exponentials[edit]
54.
55.
56.
57.
Logarithms[edit]
58.
59.
60.
61.
62.
Trigonometric functions[edit]
63.
64.
More Differentiation[edit]
65.
66.
67.
68.
69.
70.
71.
72.
73.
Implicit Differentiation[edit]
Use implicit differentiation to find y'
74.
75.
Logarithmic Differentiation[edit]
Use logarithmic differentiation to find :
76.
77.
78.
79.
80.
Equation of Tangent Line[edit]
For each function, , (a) determine for what values of the tangent line to is horizontal and (b) find an equation of the tangent line to at the given point.
81.
82.
83.
84.
85.
86.
87. Find an equation of the tangent line to the graph defined by at the point (1,-1).
88. Find an equation of the tangent line to the graph defined by at the point (1,0).
Higher Order Derivatives[edit]
89. What is the second derivative of ?
90. Use induction to prove that the (n+1)th derivative of a n-th order polynomial is 0.