Derivatives Chapter 3

Find  $\frac{dy}{dx}$  .    

 $y=\frac{3}{2}x^5+2x^3-\frac{5}{3}x^2$  

•  $\frac{dy}{dx}=\frac{15}{2}x^4+6x^2-\frac{10}{3}x^{ }$  

•  $\frac{dy}{dx}=\frac{15}{2}x^2+6x^3-\frac{10}{3}x^{ }$  

•  $\frac{dy}{dx}=\frac{3}{2}x^4+2x^2-\frac{5}{3}x$  

•  $\frac{dy}{dx}=\frac{15}{2}x+6x-\frac{10}{3}x^{ }$  

Find  $\frac{dy}{dx}$  

 $y=\left(3x^2+3\right)\left(5x^2+3\right)$   

•  $\frac{dy}{dx}=60x^3+48x$  

•  $\frac{dy}{dx}=30x^3+18x$  

•  $\frac{dy}{dx}=3x^2+6x+3$  

•  $\frac{dy}{dx}=15x^4+84x^2+9$  

Find  $\frac{dy}{dx}$  . 

  $y=\frac{5x^2+4}{4x^2+5}$  

•  $\frac{dy}{dx}=\frac{18x}{\left(4x^2+5\right)^2}$  

•  $\frac{dy}{dx}=\frac{18x}{4x^2+5}$  

•  $\frac{dy}{dx}=\frac{40x^3+32x}{\left(4x^2+5\right)^2}$  

Find y'.

 $y=5x^2\sec x$  

•  $y'=10x\sec x+5x^2\sec x\tan x$  

•  $y'=5x\sec^2x+10x\sec x\tan x$  

•  $y'=10x\sec x\tan x$  

•  $y'=5x^2\sec x+10x\sec x\tan x$  

 $y=x^2\sin x\ +\ \cos x$  

Find y'.

•  $y'=\left(2x-1\right)\sin x+x^2\cos x$  

•  $y'=x\sin x+\cos x$  

•  $y'=2x\cos x-\sin x$  

•  $y'=2x\sin x+\cos x-x^2\sin x$  

Find the derivative.

 $y=\frac{1}{x^2}$  

•  $y'=-2x$  

•  $y'=-\frac{2}{x^3}$  

•  $y'=2x$  
  

•  $y'=\frac{x}{2}$ 

Find the derivative.

y = x⁴ tan x

• y' = x⁴ sec²x - 4x³tanx

• y' = x⁴ sec²x + 4x³tanx

• y' = 4x³sec²x

• y' = -4x³ tanx

Find the derivative y = tanxcosx

• y ' = sec²xcosx - tanxsinx

• y ' = sec²xcosx + tanxsinx

• y ' = sec²xsinx

• y ' = sec²xcosx - tanxcosx

Find the derivative

y = 5sinx + 3x³cosx

• y' = -5cosx − 3x³sinx + 9x²cosx

• y' = 5sinx − 3x³sinx + 9x²cosx

• y' = 5cosx − 3x³sinx + 9x²cosx

• y' = 5cosx + 3x³sinx + 9x²cosx

A particle moves along a horizontal line. It's position function, s(t) = t³ -11t² + 24t , measured in feet. Find the displacement over interval of time 1 < t < 5 seconds.

• -44 feet

• 116 feet

• 236 feet

• -176 feet