Derivatives Basic Rules

The derivative of a function at a given point,  $c$  , is equal to which of the following

• The slope of the secant line through c

• The slope of the vertical line through c

• The slope of the horizontal line through c

• The slope of the line tangent to the function at c

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?

•  $h'\left(x\right)=3$  

•  $q'\left(x\right)=3$  

•  $b'\left(x\right)=3$  

•  $f'\left(x\right)=3$  

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What is the derivative of 0?

• You can't take the derivative of 0.

• 0

• This is all derivative.

• Any constant

 $If\ f\left(x\right)=\sin\left(x\right),\ then\ f'\left(x\right)\ =\ ?$  

•  $\sin\left(x\right)$  
  

•  $\cos\left(x\right)$  
  

•  $-\sin\left(x\right)$  
  

•  $-\cos\left(x\right)$  
  

Tags

CCSS.HSF.TF.A.4

 $If\ f\left(x\right)=\cos\left(x\right),\ then\ f'\left(x\right)=?$  

•  $\sin\left(x\right)$  
  

•  $\cos\left(x\right)$  
  

•  $-\sin\left(x\right)$  
  

•  $-\cos\left(x\right)$  
  

Tags

CCSS.HSF.TF.A.2

If  $f\left(x\right)=e^x,\ then\ f'\left(x\right)=?$  

•  $\ln\left(x\right)$  
  

•  $e^x$  
  

•  $-e^x$  
  

•  $\frac{1}{e^x}$  

Tags

CCSS.HSF.BF.B.5

 $If\ y=e^{5x},\ then\ \frac{dy}{\text{d}x}=?$  

•  $e^x$  

•  $e^{5x}$  

•  $5e^x$  

•  $5e^{5x}$  

 $If\ y=8^x,\ then\ \frac{dy}{dx}=?$  

•  $\left(\ln8\right)8^x$  

•  $\frac{1}{\ln8}8^x$  

•  $8^x$  

•  $\frac{1}{\left(\ln8\right)\left(8^x\right)}$  

Tags

CCSS.HSF-IF.C.8B