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AP Calculus Basic Derivatives with trig (no e, lnx) Flashcards | StudBud
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AP Calculus Basic Derivatives with trig (no e, lnx)
AP Calculus Basic Derivatives with trig (no e, lnx)
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Power Rule and Graphs of Derivatives
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Questions
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Answers
1
derivative using quotient rule
x12
8x7
x20
x10
2
Find the derivative using power rule
10x4-6x+9x-2-3
2x6-3x3+9x-3-3
10x5-3x2-9x-2
2x4-6x2-9x-3
3
Find derivative using product rule
h'(x)=192x3+276x2+28x+19
h'(x)=4x2+31x+1
h'(x)=48x3+66x2+52x+11
h'(x)=146x2-38x+4
4
Find the derivative of f(x) = 7x
-1
f ' (x) = -7x
f ' (x) = -7x-2
f ' (x) = 7x-2
f ' (x) = -7x-1
5
Let f (x) = x
4
+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
7
3
10
4
6
What is the correct product rule formula?
fI(x)= gI(x)*f(x)
fi(x)= (gI(x)*fi(x))-(f(x)*g(x))
fI(x)= (g(x)*fI(x))+(f(x)*gI(x))
fI(x)= f(x)*g(x)
7
Solve
this Power Rule Derivative Problem:
4x
3
+9x
2
-(5/x)
7x2+11x+5/x
12x2+18x+5/x2
12x2+16x+5/x2
12x2+18x+5/x
8
Trig Derivatives
sin (x)
- sec (x)
sec (x)
- sin (x)
9
Which describes the Power Rule for derivatives?
(n-1)xn-1
nxn-1
xn-1
nxn
10
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
-16
-24
16
24
11
Determine the x-value(s), if any, at which f (x) = x
3
+ 6x - 2 has a horizontal tangent.
x = 2
x = -2
The graph has no horizontal tangents
x = 3
12
Find derivative using product rule
f'(x)=-6x2-13x+4
f'(x)=22x2+13x+4
f'(x)=-12x2-8
f'(x)=36x2+12x+4
13
Trig Derivatives
-csc (x) cot (x)
sec2 (x)
-csc2 (x)
sec (x) tan (x)
14
Let f (x) = 6x
1/2
. What is the instantaneous rate of change at x = 4?
6
3
3/2
3/4
15
Trig Derivatives
-csc (x) cot (x)
sec (x) tan (x)
-csc2 (x)
sec2 (x)
16
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 8x-1/2 + 2
f ' (x) = 2x1/2
f ' (x) = 2x-1/2
f ' (x) = 8x-1/2
17
At which x - value(s) is the graph shown not differentiable?
x = 0 and x =1
x =1
x = 0
x = -2 and x = 2
18
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x3
f ' (x) = 12x3 + 5x
f ' (x) = 4x2 + 5
f ' (x) = 4x3 + 5
19
Quotient Rule?
(F/g)’=(f’g+g’f)/g2
(F/g)’=(f’g-g’f)/g2
(fg)’=f’g+g’f
(fg)’=f’g-g’f
20
Trig Derivatives
sec (x) tan (x)
-csc (x) cot (x)
sec2 (x)
- csc2 (x)
