[Problem Set 3.2] Basic Differentiation Rules

Find the derivative:

 $f\left(x\right)=15$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=1$  

•  $f'\left(x\right)=15$  

Find the derivative:

 $f\left(x\right)=-\frac{5}{3}$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=-1$  

•  $f'\left(x\right)=-\frac{5}{3}$  

Find the derivative:

 $f\left(x\right)=15^{-2}$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=-2\left(15\right)^{-3}$  

•  $f'\left(x\right)=-15$  

Find the derivative:

 $f\left(x\right)=5x$  

•  $f'\left(x\right)=5$  

•  $f'\left(x\right)=5x$  

•  $f'\left(x\right)=0$  

Find the derivative:

 $f\left(x\right)=-10x$  

•  $f'\left(x\right)=-10$  

•  $f'\left(x\right)=-10x$  

•  $f'\left(x\right)=-20x^2$  

Find the derivative:

 $f\left(x\right)=\frac{3}{5}x$  

•  $f'\left(x\right)=\frac{3}{5}$  

•  $f'\left(x\right)=-\frac{5}{3}x$  

•  $f'\left(x\right)=-3x^5$  

Find the derivative:

 $f\left(x\right)=x-1$  

•  $f'\left(x\right)=1$  

•  $f'\left(x\right)=-1$  

•  $f'\left(x\right)=-x$  

Find the derivative:

 $f\left(x\right)=5-3x$  

•  $f'\left(x\right)=-3$  

•  $f'\left(x\right)=5$  

•  $f'\left(x\right)=2x$  

Find the derivative:

 $f\left(x\right)=4x^2$  

•  $f'\left(x\right)=8x$  

•  $f'\left(x\right)=4x$  

•  $f'\left(x\right)=x^2$  

Find the derivative:

 $f\left(x\right)=-8x^3$  

•  $f'\left(x\right)=-24x^2$  

•  $f'\left(x\right)=3x^{-24}$  

•  $f'\left(x\right)=-8x^4$