Derivatives - Power Rule

Which of the following is NOT an acceptable notation for writing "the derivative of the function f(x)?"

• $f'\left(x\right)$

• $\frac{d}{dx}f\left(x\right)$

• $y'$

• $\frac{df}{dx}\left(x\right)$

Which of the following is NOT a definition of "the derivative of the function f(x)"

• The instantaneous rate of change of the function with respect to x

• The rate of change of a variable (y) with respect to the rate of change of another variable (x)

• The limit of the function f(x) as the slope of the tangent line becomes 0

• The slope of the tangent line to the function at a given value of x

Find the derivative of the given equation: $f\left(x\right)=-4x$ 

•  $f'\left(x\right)=4$  

•  $f'\left(x\right)=x$  

•  $f'\left(x\right)=-4$  

•  $f'\left(x\right)=0$  

Find the derivative of the given equation: $f\left(x\right)=7$ 

•  $f'\left(x\right)=\frac{7}{x}$  

•  $f'\left(x\right)=0$  

•  $f'\left(x\right)=7x$  

•  $f'\left(x\right)=-\frac{7}{x}$  

Find the derivative of the given equation: $f\left(x\right)=12-8x$  

•  $f'\left(x\right)=12-8x^2$ 

•  $f'\left(x\right)=-8x^2$ 

•  $f'\left(x\right)=-8$ 
  

•  $f'\left(x\right)=4$ 
  

Find the derivative of the given function: $f\left(x\right)=x^4$ 

•  $f\left(x\right)=x^3$  

•  $f'\left(x\right)=4x$  

•  $f'\left(x\right)=4x^3$  

•  $f\left(x\right)=4x^4$  

Find the derivative of the function: $f\left(x\right)=-\frac{10}{3}$  

•  $f'\left(x\right)=-\frac{10}{3x}$  

•  $f'\left(x\right)=-\frac{10x}{3}$  

•  $f'\left(x\right)=\frac{10x}{3}$  

•  $f'\left(x\right)=0$  

Find the derivative of the given function: $f\left(x\right)=1-x^2$ 

•  $f'\left(x\right)=1-2x$  

•  $f'\left(x\right)=-2x$  

•  $f'\left(x\right)=-2$  

•  $f'\left(x\right)=0$  

Tags

CCSS.HSF-IF.C.8B

Find the derivative of the given function: $f\left(x\right)=x^3+x^2+3$ 

•  $f'\left(x\right)=3x^2+2x$  

•  $f'\left(x\right)=5x$  

•  $f'\left(x\right)=5x+3$  

•  $f'\left(x\right)=x^3+x^2$  

Find the derivative of the given function:
 $f\left(x\right)=\frac{1}{x^2}$ 

•  $f'\left(x\right)=\frac{1}{2x}$  

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

•  $f'\left(x\right)=-\frac{2}{x}$  

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

Tags

CCSS.HSF-IF.C.8B