AP Calc AB Review for QZ 09-10

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line

 $\frac{\text{d}}{\text{d}x}\left(\sin x\right)=$  

•  $\cos x$ 

•  $-\cos x$  
  

•  $-\sin x\cos x$  

•  $\sin x\cos x$  
  

 $\frac{d}{dx}\left(\cos x\right)=$  

•  $\sin x$  
  

•  $-\sin x$  

•  $-\csc x\cot x$  

•  $\sec2x$  

 $\frac{d}{dx}\left(\tan x\right)=$  

•  $\csc x\cot x$ 

•  $\sec x\tan x$ 

•  $\sec^2x$  

•  $-\csc x\cot x$ 

 $\frac{d}{dx}\left(\csc x\right)=$  

•  $\sec x\tan x$  

•  $\sec^2x$ 

•  $\csc x\cot x$ 

•  $-\csc x\cot x$ 

 $\frac{d}{dx}\left(\sec x\right)=$  

•  $\sec x\tan x$  

•  $-\sec x\tan x$ 

•  $\tan^2x$ 

•  $\csc x\cot x$ 

 $\frac{d}{dx}\left(\cot x\right)=$  

•  $-\csc x\cot x$ 

•  $\csc x\cot x$ 

•  $-\csc^2x$ 

•  $\csc^2x$  

If  $f\left(x\right)=x^4\sin x$ , find  $f'\left(x\right)$ .

•  $x^4\cos x-4x^3\sin x$ 

•  $x^4\cos x+4x^3\sin x$  

•  $4x^3\cos x$ 

•  $-4x^3\cos x$  

Find  $f'\left(x\right)$  if  $f\left(x\right)=\tan x\cos x$ 

•  $f'\left(x\right)=\sec^2x\cos x-\tan x\sin x$ 

•  $f'\left(x\right)=\sec^2x\cos x+\tan x\sin x$ 

•  $f'\left(x\right)=\sec^2x\sin x$ 

•  $f'\left(x\right)=\sec^2x\cos x-\tan x\cos x$ 

Find  $y'$  if  $y=\cos^5\left(4x^3\right)$ .

•  $-5\cos^4\left(4x^3\right)\sin\left(12x^2\right)$ 

•  $-60x^2\sin^4\left(4x^3\right)$ 

•  $-5\cos^4\left(4x^3\right)\sin\left(4x^3\right)$ 

•  $-60x^2\cos^4\left(4x^3\right)\sin\left(4x^3\right)$