Derivatives Quiz

Find the derivative

 $f\left(x\right)=3x^3-9x^2+11x-2$  

•  $f'\left(x\right)=9x^2-18x+11$  

•  $f'\left(x\right)=9x^3-18x^2+11$  

•  $f'\left(x\right)=3x^2-9x+11$  

•  $f'\left(x\right)=9x-18$  

Evaluate:

 $\frac{d}{dx}\left[\cos x-\sin x\right]$  

•  $=-\sin x-\cos x$  

•  $=\sin x-\cos x$  

•  $=-\sin x+\cos x$  

•  $=\sin x+\cos x$  

Find

 $\frac{d^2y}{dx^2}$   given
  $y=x^3-2x^2+11x-9$  

•  $3x^2-4x+11$  

•  $6x-4$  

•  $6$ 

•  $0$  

Use the product rule to find the derivative of
 $f\left(x\right)=x^2\sin x$  

•  $f'\left(x\right)=2x\cos x$  

•  $f'\left(x\right)=2x\sin x+x^2\cos x$  

•  $f'\left(x\right)=2x\sin x-x^2\cos x$  

•  $f'\left(x\right)=x\sin x+x^2\cos x$  

If the position of a falling object is
 $s\left(t\right)=-16t^2-20t+45$  
then  what is its velocity equation?

•  $v\left(t\right)=-32t-20$  

•  $v\left(t\right)=-32t$  

•  $v\left(t\right)=-32$  

•  $v\left(t\right)=-32t+20$  

If the position of a falling object is
 $s\left(t\right)=-4.9t^2-8t+10$  
then  what is its acceleration equation?

•  $a\left(t\right)=-9.8t-8$  

•  $a\left(t\right)=-9.8t$  

•  $a\left(t\right)=-9.8$  

•  $a\left(t\right)=-4.9$  

Use any method you want to find the derivative of
 $g\left(x\right)=\left(2x-3\right)\left(x+9\right)$  

•  $g'\left(x\right)=2x^2+15x-27$  

•  $g'\left(x\right)=4x+15$  

•  $g'\left(x\right)=2$  

•  $g'\left(x\right)=2x$  

Use division to find the derivative of
 $h\left(x\right)=\frac{x^3-9x+4}{x}$  

•  $h'\left(x\right)=x^2-9+4x^{-1}$  

•  $h'\left(x\right)=2x-\frac{4}{x^2}$  

•  $h'\left(x\right)=2x+\frac{4}{x^2}$  

•  $h'\left(x\right)=2x-\frac{4}{x}$  

Differentiate:
 $y=x^{\frac{2}{3}}+4x^{\frac{1}{4}}$  

•  $\frac{dy}{dx}=\frac{2}{3x^{\frac{1}{3}}}+\frac{1}{x^{\frac{3}{4}}}$  

•  $\frac{dy}{dx}=-\frac{2}{3x^{\frac{1}{3}}}+\frac{1}{x^{\frac{3}{4}}}$  

•  $\frac{dy}{dx}=\frac{2}{3x^{\frac{1}{3}}}-\frac{1}{x^{\frac{3}{4}}}$  

•  $\frac{dy}{dx}=-\frac{2}{3x^{\frac{1}{3}}}-\frac{1}{x^{\frac{3}{4}}}$  

Find the derivative:
 $f\left(x\right)=\frac{1}{x}-\frac{1}{x^2}+\frac{1}{x^3}$  

•  $f'\left(x\right)=x^{-1}-x^{-2}+x^{-3}$  

•  $f'\left(x\right)=-\frac{1}{x^2}+\frac{2}{x^3}-\frac{3}{x^4}$  

•  $f'\left(x\right)=\frac{1}{x^2}+\frac{2}{x^3}-\frac{3}{x^4}$  

•  $f'\left(x\right)=-\frac{1}{x^2}-\frac{2}{x^3}-\frac{3}{x^4}$