Derivatives Memory Quiz

For the function below, identify its derivative:

 $y=e^x$  

•  $\frac{dy}{dx}=e^x$  

•  $\frac{dy}{dx}=\ln x$  

•  $\frac{dy}{dx}=xe^{x-1}$  

•  $\frac{dy}{dx}=e^x\ln x$  

For the function below, identify its derivative:

 $y=f\left(x\right)\cdot g\left(x\right)$  
Assume all functions are individually differentiable.

•  $\frac{dy}{dx}=f'\left(x\right)\cdot g\left(x\right)+g'\left(x\right)\cdot f\left(x\right)$  

•  $\frac{dy}{dx}=f'\left(x\right)\cdot g'\left(x\right)$  

•  $\frac{dy}{dx}=\frac{f'\left(x\right)\cdot g'\left(x\right)+g'\left(x\right)\cdot f\left(x\right)}{\left[g\left(x\right)\right]^2}$  

•  $\frac{dy}{dx}=\frac{f'\left(x\right)\cdot g'\left(x\right)-g'\left(x\right)\cdot f\left(x\right)}{\left[g\left(x\right)\right]^2}$  

For the function below, identify its derivative:

 $y=\sin x$  

•  $\frac{dy}{dx}=\sin x$  

•  $\frac{dy}{dx}=-\cos x$  

•  $\frac{dy}{dx}=\cos x$  

•  $\frac{dy}{dx}=\sec x\tan x$  

For the function below, identify its derivative:

 $y=a^x$  
Given that a is a real number, and a > 0.

•  $\frac{dy}{dx}=a^x$  

•  $\frac{dy}{dx}=xa^{x-1}$  

•  $\frac{dy}{dx}=xa^{x-1}\cdot\ln a$  

•  $\frac{dy}{dx}=a^x\ln a$  

Tags

CCSS.HSF.BF.B.5

For the function below, identify its derivative:

 $y=\csc x$  

•  $\frac{dy}{dx}=\csc^2x$  

•  $\frac{dy}{dx}=-\csc x\cot x$  

•  $\frac{dy}{dx}=\csc x\cot x$  

•  $\frac{dy}{dx}=-\csc^2x$  

For the function below, identify its derivative:

 $y=\sec x$  

•  $\frac{dy}{dx}=\sec^2x$  

•  $\frac{dy}{dx}=-\sec x\tan x$  

•  $\frac{dy}{dx}=\sec x\tan x$  

•  $\frac{dy}{dx}=-\sec^2x$  

For the function below, identify its derivative:

 $y=f\left(g\left(x\right)\right)$  
Assume all functions are individually differentiable.

•  $\frac{dy}{dx}=f'\left(x\right)\cdot g\left(x\right)+g'\left(x\right)\cdot f\left(x\right)$  

•  $\frac{dy}{dx}=f'\left(g\left(x\right)\right)\cdot g'\left(x\right)$  

•  $\frac{dy}{dx}=f'\left(g'\left(x\right)\right)$  

•  $\frac{dy}{dx}=\frac{f'\left(x\right)\cdot g'\left(x\right)-g'\left(x\right)\cdot f\left(x\right)}{\left[g\left(x\right)\right]^2}$  

Tags

CCSS.HSF.IF.A.2

For the function below, identify its derivative:

 $y=x^n$  
Given that n is a real number.

•  $\frac{dy}{dx}=nx^{n-1}$  

•  $\frac{dy}{dx}=nx^n$  

•  $\frac{dy}{dx}=x^{n-1}$  

•  $\frac{dy}{dx}=\frac{1}{n+1}x^{n+1}$  

For the function below, identify its derivative:

 $y=\cos x$  

•  $\frac{dy}{dx}=-\sin x$  

•  $\frac{dy}{dx}=-\cos x$  

•  $\frac{dy}{dx}=\sin x$  

•  $\frac{dy}{dx}=-\csc x\cot x$  

For the function below, identify its derivative:

 $y=\frac{f\left(x\right)}{g\left(x\right)}$  
Assume all functions are individually differentiable.

•  $\frac{dy}{dx}=\frac{f'\left(x\right)\cdot g\left(x\right)-g'\left(x\right)\cdot f\left(x\right)}{g\left(x\right)'}$  

•  $\frac{dy}{dx}=\frac{f'\left(x\right)\cdot g\left(x\right)+g'\left(x\right)\cdot f\left(x\right)}{\left[g\left(x\right)\right]^2}$  

•  $\frac{dy}{dx}=\frac{f'\left(x\right)}{g'\left(x\right)}$  

•  $\frac{dy}{dx}=\frac{f'\left(x\right)\cdot g\left(x\right)-g'\left(x\right)\cdot f\left(x\right)}{\left[g\left(x\right)\right]^2}$  

Tags

CCSS.HSA.APR.D.7