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Calculus (DERIVATIVES) Flashcards | StudBud
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Calculus (DERIVATIVES)
Calculus (DERIVATIVES)
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Answers
1
What derivative rule can be used for this example? \frac{d}{dx}\left[x^4\right]
chain rule
product rule
quotient rule
power rule
2
\frac{d}{dx}\left[\ln\right]=?
\frac{1}{x\ln b}\cdot b^x
\frac{1}{x\ln b}
none of the above
\frac{1}{x}
3
What is the value of the following limit ? \lim_{x\to0}\frac{\sin x}{x}=?
∅
none of the above
1
0
4
\frac{d}{dx}\left[\cos x\right]=?
-\sin x
\cot x
\cos^2x
none of the above
5
\frac{d}{dx}\left[f^{-1}\left(x\right)\right]=?
\frac{1}{f'\left(f\left(x\right)\right)}
\frac{1}{f'\left(f^{-1}\left(x\right)\right)}
6
\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]= Indicates the product rule
False
True
7
Complete the formula for this derivative: \frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=?
f'\left(x\right)g\left(x\right)-g'\left(x\right)f\left(x\right)
All of the above
f'\left(x\right)g\left(x\right)+g'\left(x\right)f\left(x\right)
f'\left(x\right)g\left(x\right)-g'\left(x\right)f\left(x\right)/g(x)2
8
\lim_{h\to0}\frac{e^h-1}{h}=?
1
2
3
0
9
\frac{d}{dx}\left[\sec^{-1}x\right]=?
\frac{-1}{\left|x\right|\sqrt{x^2-1}}
\frac{1}{\sqrt{1+x^2}}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{\left|x\right|\sqrt{x^2-1}}
10
complete formula for the following derivative rule: \frac{d}{dx}\left[f\left(g\left(x\right)\right)\right]=?
f'\left(g\left(x\right)\right)+g'\left(x\right)
None of the above
f'\left(g\left(x\right)\right)\cdot g'\left(x\right)
f'\left(g\left(x\right)\right)
11
find the derivative: \frac{d}{dx}\left[x\right]=?
3
1
4
does not exist
12
What derivative rule can be used for this example?\frac{d}{dx}\left[f\left(x\right)g\left(x\right)\right]
power rule
your mom's rule
product rule
quotient rule
13
Complete the formula for this derivative rule: \frac{d}{dx}\left[x+y\right]=?
\frac{d}{dx}\left[xy\right]
none of the above
\frac{d}{dx}\left[x\right]+\frac{d}{dx}\left[y\right]
x'y+y'x
14
Complete the formula for this derivative rule: \frac{d}{dx}\left[f\left(x\right)g\left(x\right)\right]=?
f'\left(x\right)g\left(x\right)-g'\left(x\right)f\left(x\right)
f'\left(x\right)g\left(x\right)+g'\left(x\right)f\left(x\right)
15
\frac{d}{dx}\left[\sin^{-1}x\right]=?
\frac{1}{\sqrt{1-x^2}}
\frac{-1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{1+x^2}}
\frac{-1}{\sqrt{1+x^2}}
16
find the derivative: \frac{d}{dx}\left[2x^3\right]
6x3
6x2
5x3
5x2
17
\frac{d}{dx}\left[\cot^{-1}x\right]=?
\frac{-1}{\sqrt{1-x^2}}
\frac{-1}{1+x^2}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{1+x^2}
18
\frac{d}{dx}\left[\tan x\right]=?
\csc x
\sec^2x
\cot^2x
\sin x
19
\frac{d}{dx}\left[\sec x\right]=?
\sec x\tan x
\sec^2x
\cos^2x
-\csc x\cot x
20
What derivative rule can be applied with this example? \frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]
product rule
power rule
quotient rule
none of the above
21
\frac{d}{dx}\left[b^x\right]=?
\frac{1}{x\ln b}
\frac{1}{x}
\frac{b^h-1}{h}
b^x\cdot\lim_{h\to0}\frac{b^h-1}{h}
22
\lim_{x\to0}\frac{1-\cos x}{x}=?
0
1
3
2
23
What derivative rule can be used for this example? \frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]
product rule
quotient rule
power rule
sum or difference rule
24
\frac{d}{dx}\left[\cot x\right]=?
\tan^2x
-\csc^2x
\sec^2x
none of the above
25
\frac{d}{dx}\left[\log_bx\right]=?
\left(\frac{1}{x\ln b}\right)^2
\frac{1}{x}
\frac{1}{x\ln b}
none of the above
26
\frac{d}{dx}\left[\cos^{-1}x\right]=?
\frac{-1}{\sqrt{1+x^2}}
\frac{-1}{\sqrt{1-x^2}}
27
What derivative rule can be used for this example? \frac{d}{dx}\left[f\left(g\left(x\right)\right)\right]
power rule
product rule
chain rule
sum rule
28
\frac{d}{dx}\left[2x+3\right]=2
False
True
29
\frac{d}{dx}\left[\sqrt[4]{x}\right]=\frac{1}{4x^{\frac{3}{4}}}
False
True
30
\frac{d}{dx}\left[\csc^{-1}x\right]=?
\frac{-1}{\left|x\right|\sqrt{x^2-1}}
none of the above
\frac{1}{\left|x\right|\sqrt{x^2-1}}
\frac{1}{\sqrt{1-x^2}}
31
\frac{d}{dx}\left[\csc x\right]=?
\sin^2x
\cos^2x
-\csc x\cot x
\sec x\tan x
32
\frac{d}{dx}\left[\tan^{-1}x\right]=?
\frac{-1}{1+x^2}
\frac{1}{\sqrt{1-x^2}}
\frac{1}{\sqrt{x^2-1}}
\frac{1}{1+x^2}
33
\frac{d}{dx}\left[\sin x\right]=?
cos(x)
csc(x)
tan(x)
sin2 x
34
\lim_{x\to0}\frac{\sin x}{x}=∅
True
False
