Basic Differentiation Rules

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

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x^2+2x^2-x$  

Which of the following is the correct definition of the Power Rule of derivatives?

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=x^{n-1}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=nx^{n-1}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{x^{n-1}}{n}$

• Given $f\left(x\right)=x^n$ , $f'\left(x\right)=\frac{n}{x^{n-1}}$

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

•  $h'\left(x\right)=3$  

•  $q'\left(x\right)=3$  

•  $b'\left(x\right)=3$  

•  $f'\left(x\right)=3$  

What is the derivative of 0?

• You can't take the derivative of 0.

• 0

• This is all derivative.

• Any constant

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

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

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

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

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

Tags

CCSS.HSF-BF.A.1A

Find $\frac{dy}{dx}$  for $y=x^8+2x^6-x^3-4x$  

•  $\frac{dy}{dx}=8x^7-12x^5-3x^2-4x$  

•  $\frac{dy}{dx}=8x^7+12x^5-3x^2-4$  

•  $\frac{dy}{dx}=8x^7+12x^5+3x^2+4x$  

•  $\frac{dy}{dx}=8x^7-12x^5+3x^2+4$  

Find the derivative for $f\left(x\right)=\left(x+2\right)\left(x^2-3\right)$  

•  $f'\left(x\right)=3x^2-3+4x$  

•  $f'\left(x\right)=3x^2-3x+4x-6$  

•  $f'\left(x\right)=3x^2-3+4x-6$  

•  $f'\left(x\right)=x^3-3x+2x^2-6$  

Find the derivative for $y=\frac{2x^5+x-4}{x^3}$  

•  $\frac{dy}{dx}=4x^2-\frac{2}{x^2}+\frac{12}{x^3}$  

•  $\frac{dy}{dx}=4x-\frac{2}{x^3}+\frac{12}{x^4}$  

•  $\frac{dy}{dx}=4x^2+\frac{2}{x^3}-\frac{12}{x^4}$  

•  $\frac{dy}{dx}=4x+\frac{1}{2x^3}-\frac{12}{x^4}$  

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

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x+2$  

•  $f'\left(x\right)=6x^2+2$  

•  $f'\left(x\right)=6x^2+2x^2-x$