AP Calculus BC Unit 2- Derivatives Flashcards | StudBud

AP Calculus BC Unit 2- Derivatives

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Questions 14

Answers

1
f\left(x\right)=\cos\left(x\right)\cdot e^x
\cos\left(x\right)-e^x\sin\left(x\right)
e^x\left(\cos\left(x\right)-\sin\left(x\right)\right)
e^x\cos\left(x\right)+\sin\left(x\right)
e^x\left(\cos\left(x\right)+\sin\left(x\right)\right)
2
f'\left(x\right)=?,f\left(x\right)=5x^4-3x^{-1}
20x^3+3x^2
20x^3+\frac{3}{x^2}
20x^3-3x^{-2}
20x^3+3
3
\frac{d}{dr}\left(r^{\frac{3}{2}}+r\right)
\frac{3}{2}r^{\frac{1}{2}}+1
1
\frac{3}{2}r^{\frac{3}{2}}+1
DNE
4
What is the derivative of \frac{\ln\left(x\right)}{x}?
\frac{-1-\ln\left(x\right)}{x^2}
\frac{1}{x^2}-\frac{\ln\left(x\right)}{x^2}
\frac{1-\ln\left(x\right)}{x^2}
\frac{1+\ln\left(x\right)}{x^2}
5
f'\left(x\right)=?,g\left(x\right)=3x^2+9x+1
6x+9
6x^2
Cannot be determined
6x^2+9
6
What is the derivative of 3\left(-8x^2+9\right)^5?
-48x\left(-8x^2-9\right)^4
-80x\left(-8x^2-9\right)^4
-240x\left(-8x^2-9\right)^4
-16x\left(-8x^2-9\right)^4
7
f'\left(x\right)=?,f\left(x\right)=\frac{x^2+6x+9}{x+3}?
6
3
1
x
8
f'\left(x\right)=?,f\left(x\right)=\arctan\left(x\right)
\frac{-1}{1+x^2}
\frac{1}{1+x^2}
\frac{1}{\sqrt{1-x^2}}
\frac{-1}{\sqrt{1-x^2}}
9
What is the derivative of \sec\left(x\right)?
sec(x)tan(x)
\frac{1}{\cos^2\left(x\right)}
\sec^2\left(x\right)
cos(x)
10
\frac{d}{dx}\left(5^x\right)
\frac{5^x}{\ln\left(5\right)}
5\cdot5^{x-1}
\ln\left(5\right)\cdot5^x
5^{x-1}
11
\frac{d}{dx}\left(\log_2x\right)
\frac{\ln\left(2\right)}{x\log_2\left(x\right)}
\frac{1}{x\log\left(2\right)}
\frac{\ln\left(2\right)}{x}
\frac{1}{x\ln\left(2\right)}
12
f'\left(x\right)=?,f\left(x\right)=12x^4-5x^3+\frac{11}{2}x-9
48x^3-15x^2-\frac{11}{2}
48x^3-15x^2+\frac{11}{2}+9
48x^3+15x^2+\frac{11}{2}
48x^3-15x^2+\frac{11}{2}
13
f'\left(x\right)=?,f\left(x\right)=\frac{5x^2+1}{\left(5x^4\right)\left(2x+1\right)}
\frac{-2\left(15x^3+5x^2+5x+2\right)}{5x^8\left(2x+1\right)^2}
\frac{-2\left(15x^3+5x^2+5x+2\right)}{5x^5\left(2x+1\right)^2}
\frac{2\left(15x^3+5x^2+5x+2\right)}{5x^8\left(2x+1\right)^2}
\frac{-2\left(15x^3-5x^2-5x+2\right)}{5x^5\left(2x+1\right)^2}
14
f'\left(x\right)=?,f\left(x\right)=\sqrt{x}\left(2x^{\frac{5}{2}}+x^{\frac{1}{2}}\right)
\frac{-\left(2x^{\frac{5}{2}}+x^{\frac{1}{2}}\right)}{\sqrt{x}}
6x^2+1
3x^2+x
2x^3+x