Basic Differentiation Rules

Given  $f\left(x\right)=3x^2+2x-1$  , which of the following is the correct derivative?

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x^2+2x^2-x$  

Find the slope of the tangent line of the graph of  $f\left(x\right)=x^2-4x$  at the point (-2, 12) ?

•  $m=8$  
  

•   $m=-8$ 

•  $m=-4$  

•  $m=4$  

Given $f\left(x\right)=17$  , what is the derivative of  $f\left(x\right)$  ?

•  $f'\left(x\right)=17x$  

•  $f'\left(x\right)=17$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=17x^2$  

Given $f\left(x\right)=\frac{2x^2+4x-6}{4x}$  , find  $f'\left(x\right)$  .

•  $f'\left(x\right)=\frac{4x+4}{4}$  

•  $f'\left(x\right)=x+1$  

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

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

Tags

CCSS.HSA.APR.D.6

Given $f\left(x\right)=3x$  , which of the following is the derivative of the function?

•  $h'\left(x\right)=3$  

•  $q'\left(x\right)=3$  

•  $b'\left(x\right)=3$  

•  $f'\left(x\right)=3$  

Differentiate with respect to x.

• 
• 
• 
• 

Differentiate with respect to x. $y=\frac{1}{x^3}$  

•  $\frac{\partial y}{\partial x}=\frac{1}{x^4}$  

•  $\frac{\partial y}{\partial x}=-3x$  

•  $\frac{\partial y}{\partial x}=-\frac{3}{x^3}$  

•  $\frac{\partial y}{\partial x}=-\frac{3}{x^4}$  

Find the equation of the tangent line of the graph of $f\left(x\right)=3x-2x^2$  at the point (2, -2) ?

• y=5x-8

• y=-5x+8

• y=8x-5

• y=-5x-12

Differentiate with respect to x.

• 
• 
• 
• 

Differentiate with respect to x.

• 
• 
• 
•