Derivatives and Antiderivatives-Quiz-Review

FInd the derivative:
 $f\left(x\right)=4x^3-2x+1$  

•  $12x^2-2$  

•  $x^4-x^2$  

•  $x^4-x^2+x$  

•  $12x-2$  

• None of the above

 Find the derivative:
 $y=5+e^{4x}$ 

•  $e^{4x}$  

•  $5e^{4x}$  

•  $4e^{4x}$  

•  $4e^x$  

• None of the above

Find the derivative:
 $y=6\sqrt{x}$  

•  $\frac{6}{\sqrt{x}}$  

•  $\frac{12}{\sqrt{x}}$  

•  $4x^{1.5}$  

•  $\frac{1}{3\sqrt{x}}$  

• None of the above

FInd the antiderivative:
 $f\left(x\right)=4x^3-2x+1$  

•  $12x^2-2+C$  

•  $x^4-x^2+C$  

•  $x^4-x^2+x+C$  

•  $12x-2+C$  

• None of the above

 Find the anti-derivative:
 $f\left(x\right)=\frac{1}{x^2+1}$ 

•  $\ln\left(1+x^2\right)+C$  

•  $\frac{1}{2x}\ln\left(1+x^2\right)+C$  

•  $2x\tan^{-1}x+C$  

•  $\tan^{-1}x+C$  

• None of the above

∫(4 - 18x)dx

• F(x) = -18
• F(x) = 4x - 9x²
• F(x) = 4x - 9x² + C
• F(x) = (4 - 18x)² /2 + C

∫ t⁶ dt

• 6t⁵
• 6t⁵ + C
• 1/7 t⁷ + C
• t⁷ + C

∫ 1/x dx

• ln x
• ln x + C
• -1/x²
• -1/x² + C

f'(x) = (x + 2)/(3x). f(x) =

• (2/3)ln|x| + x/3 + C
• 2ln|3x| + x/3 + C
• (2/3)ln|x| + C
• (2/3)ln|3x| + C

Given v(t) = x^-9, find the general equation for the antiderivative.

• (1/8)x^-8 + C
• (-1/8)x^-8 + C
• (1/10)x¹⁰
• (-1/8)x^-8