Test 2 Flashcards
1
Q
When does the derivative not exist?
A
- When the right sided limit does not equal the left sided limit (point)
- When f(x) is not defined at x=a
- When f(x) is not continuous at x=a
- When there is a vertical tangent line (because the slope of a vertical tangent line is undefined)
2
Q
derivative of f(x) = k
A
f’(x) = 0
3
Q
derivative of f(x) = x^n
A
f’(x) = nx^n-1
4
Q
derivative of f(x) = kg(x)
A
f’(x) = kg’(x)
5
Q
derivative of f(x) = g(x) + s(x)
A
f’(x) = g’(x) + s’(x)
6
Q
derivative of f(x) = g(x)h(x)
A
f’(x) = g(x)h’(x) + g’(x)h(x)
7
Q
derivative of f(x) = g(x) / h(x)
A
f’(x) = h(x)g’(x) - h’(x)g(x) / h^2(x)
8
Q
derivative of sinx
A
cosx
9
Q
derivative of cosx
A
-sinx
10
Q
derivative of tanx
A
sec^2x
11
Q
derivative of secx
A
secxtanx
12
Q
derivative of cscx
A
-cscxcotx
13
Q
derivative of cotx
A
-csc^2x
14
Q
sin^2x+cos^2x
A
1
15
Q
1 + tan^2x
A
sec^2x
16
Q
1 + cot^2x
A
csc^2x
17
Q
2sinxcosx
A
sin2x
18
Q
cos2x
A
cos^2x-sin^2x
2cos^2x-1
1-2sin^2x
19
Q
0
A
(1,0)
20
Q
π / 6
A
√3/2, 1/2
21
Q
π / 4
A
√2/2, √2/2
22
Q
π / 3
A
1/2, √3/2
23
Q
π / 2
A
0, 1
