Unit 3 Review

Mathematical Equivalence

ON

Tags

CCSS.HSF.TF.A.2

What is the derivative of cos(x)?

• sin(x)
• -sin(x)
• cos(x)
• -cos(x)

Find dy/dx

 $xy=\sin x+y^2$  

•  $\cos x+2y$  

•  $\frac{\left(\cos x-y\right)}{2y}$  

•  $\frac{\left(\cos x-y\right)}{\left(1-2y\right)}$  

•  $\frac{\left(\cos x\ +2y\right)}{\left(x-y\right)}$  

•  $\frac{\left(\cos x-y\right)}{\left(x-2y\right)}$  

Find y'

 $y=\sec^{-1}\sqrt{x}$  

•  $\frac{1}{2x\sqrt{x-1}}$  

•  $\frac{1}{\sqrt{x^2-x}}$  

•  $\frac{1}{2x\sqrt{x^2-1}}$  

•  $\frac{1}{2\sqrt{x}\left(1+x\right)}$  

•  $\frac{1}{2\sqrt{x^2-1}}$  

 $f\left(x\right)=\tan^{-1}\left(4x\right)$ 

Find the derivative of f(x).

•  $\frac{4}{16x^2+1}$  
  

•  $\frac{4}{4x^2+1}$  
  

•  $\frac{1}{16x^2+1}$  
  

•  $-\frac{1}{4x^2+1}$  
  

•  $-\frac{4}{4x+1}$  

Find dy/dx if

 $y=\ln\left(x^2+5x\right)$  

•  $\frac{2x+5}{\ln\left(x^2+5x\right)}$  

•  $\frac{2x+5}{x}$  

•  $\frac{1}{2x+5}$  

•  $\frac{2x+5}{x^2+5x}$  

•  $\left(2x+5\right)\ln\left(x^2+5x\right)$  

Find the second derivative

 $3x^2+y^3=9$  

•  $\left(\frac{2y^3-8x^2}{y^5}\right)$  

•  $-\left(\frac{2y^3+8x^2}{y^5}\right)$  

•  $-\frac{\left(-8x^2+2y^3\right)}{y^4}$  

•  $-\left(\frac{2x}{y^2}\right)$  

•  $\frac{2x^2}{3y^3}$  

Which of the following cannot be true if

 $f'\left(x\right)=7x^{\frac{4}{7}}$  

•  $f\left(x\right)=\frac{49}{11}x^{\frac{11}{7}}+\frac{15}{11}$  

•  $f"\left(x\right)=4x^{-\frac{3}{7}}$  

•  $f"\left(x\right)=\frac{4}{x^{\frac{3}{7}}}$  

•  $f'''\left(x\right)=-\frac{12}{7x^{\frac{10}{7}}}$  

•  $f'''\left(x\right)=\frac{12}{7}x^{-\frac{10}{7}}$  

• A
• B
• C
• D

• A
• B
• C
• D