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Derivative Rule Review Flashcards | StudBud
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Derivative Rule Review
Derivative Rule Review
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Review of basic derivative rules
Flashcards
15 cards
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Questions
15
Answers
1
What is the derivative of: e
x
?
e^{x-1}
1
e^x
xe^{x-1}
2
What is the derivative of: \cot\left(x^2\right) ?
2x\csc^2\left(x^2\right)
-2x\csc^2\left(x^2\right)
-\csc\left(x^2\right)\cot\left(x^2\right)
2x\sec^2\left(x^2\right)
3
What is the derivative of: 2x^4+13x^3-24x+\sqrt{x}?
8x^3+39x^2-24x+\frac{1}{2\sqrt{x}}
8x^3+39x^2-24+\frac{1}{x^2}
8x^3+39x^2-24+\frac{1}{2\sqrt{x}}
8x^3-39x^2-24x+\frac{1}{\sqrt{x}}
4
What is the derivative of: \frac{u}{v} ?
\frac{vu'-uv'}{v^2}
\frac{\left(u'-v'\right)}{v^2}
\frac{v'}{u'}
\frac{vu'+uv'}{v^2}
5
What is the derivative of: \log_2x ?
\frac{\ln2}{\ln x}
\frac{1}{x\ln2}
x\ln2
\frac{\ln x}{\ln2}
6
What is the derivative of: \frac{5}{x+1}? (Hint: Rewrite first)
\frac{-5}{\left(x+1\right)^2}
\frac{1}{5x+5}
5
\frac{5}{\left(x+1\right)^2}
7
What is the derivative of: ln(x) ?
x
ex
\frac{1}{x}
\frac{1}{\ln x}
8
What is the derivative of: csc(x) ?
csc(x)tan(x)
-cot(x)
-csc(x)cot(x)
csc(x)cot(x)
9
What is the derivative of: 4
x
?
4^x\ln4
x\cdot4^x
4^x
4\left(4^x\right)
10
What is the derivative of: \sqrt{x} ?
\frac{1}{2\sqrt{x}}
\frac{-1}{x^2}
1/x2
(\frac{1}{2}\sqrt{x}
11
What is the derivative of: x^3+7x^2-56?
3x^3+14x^2
3x^2+14x-1
3x^2+14x
3x^2+7x
12
What is the derivative of: sec(x) ?
sec2(x)
csc(x)
sec(x)tan(x)
-csc(x)
13
What is the derivative of: (u)(v) ?
u'\cdot v'
\frac{u'\cdot v'}{u\cdot v}
vu'+uv'
u'+v'
14
What is the derivative of: tan(x) ?
sin(x)cos(x)
sec2(x)
xtan(x)
tan2(x)
15
What is the derivative of: f\left(g\left(x\right)\right) ?
f'\left(g\left(x\right)\right)g'\left(x\right)
f'\left(x\right)g'\left(x\right)
g'\left(f\left(x\right)\right)f'\left(x\right)
f'\left(x\right)+g'\left(x\right)
