11.1 Derivative Rules - Quick in class check for understanding

 $f\left(x\right)=x^2+x^4$  

Calculate the derivative of the function.

•  $f'\left(x\right)=x^3+x^5$  

•  $f'\left(x\right)=x^2-4x^3$  

•  $f'\left(x\right)=6x^5$  

•  $f'\left(x\right)=2x+4x^3$  

 $g\left(x\right)=7x^3$  

Calculate the derivative of the function.

•  $g'\left(x\right)=21x^2$  

•  $g'\left(x\right)=7x^4$  

•  $g'\left(x\right)=4x^2$  

•  $g'\left(x\right)=73x^2$  

Calculate the derivative of the function.

 $g\left(x\right)=12x$  

•  $\frac{d}{dx}=12x^2$  

•  $\frac{d}{dx}=0$  

•  $\frac{d}{dx}=12$  

•  $\frac{d}{dx}=1$  

 $h\left(x\right)=15$  

Calculate the derivative of the function.

•  $h'\left(x\right)=225$  

•  $h'\left(x\right)=1$  

•  $h'\left(x\right)=15x$  

•  $h'\left(x\right)=0$  

Suppose that a company's revenue, R, and cost, C, are changing with time. Then so is the profit, P(t) = R(t) - C(t).

The rate of change of the profit is

• $P\ '\left(t\right)=R\ '\left(t\right)+C\ '\left(t\right)$

• $P\ '\left(t\right)=R\left(t\right)-C\left(t\right)$

• $P\ '\left(t\right)=R\ '\left(t\right)-C\ '\left(t\right)$

• $C\ '\left(t\right)=P\ '\left(t\right)+R\ '\left(t\right)$

Calculate the Derivative of the function.

 $f\left(x\right)=3x^2+2x-4$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=6x+2-4$  

•  $f'\left(x\right)=6x-2$  

•  $f'\left(x\right)=3x+2$  

 $g\left(x\right)=\sqrt{x}$  

Calculate the derivative of the function.

•  $g'\left(x\right)=\frac{1}{2}x^{\frac{1}{2}}$  

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

•  $g'\left(x\right)=2x^{\frac{1}{2}}$  

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