3.5 Trigonometric Derivatives Lesson

​3.5 Trigonometric Derivatives

Home

Open in new tab

Copy link

Home

Open in new tab

Copy link

Multiple Choice

#1

• cosx
• -cosx
• -sinx cosx
• sinx cosx

Multiple Choice

$$\frac{d}{dx}\left[\sin\left(2x\right)\right]$$  #2

• $$\cos\left(2x\right)$$  

• $$2\sin\left(2x\right)$$  

• $$2\cos\left(2x\right)$$  

Multiple Choice

$$\frac{d}{dx}\left(\cos x\right)=$$  #3

• $$\sin x$$  

• $$\sec x$$  

• $$-\sin x$$  

• $$-\sec x$$  

Multiple Choice

$$\frac{d}{dx}\left(\tan x\right)=$$  #4

• $$\sec x\tan x$$  

• $$\sec^2x$$  

• $$-\csc x\cot x$$  

• $$-\csc^2x$$  

Multiple Choice

$$\frac{d}{dx}\left(\csc x\right)=$$  #5

• $$\sec x\tan x$$  

• $$\sec^2x$$  

• $$-\csc x\cot x$$  

• $$-\csc^2x$$  

Multiple Choice

$$\frac{d}{dx}\left(x-3\sin x\right)=$$  #6

• $$1-3\cos x$$  

• $$1+3\cos x$$  

• $$1-3\sin x$$  

• $$1+3\sin x$$  

Multiple Choice

$$\frac{d}{dx}\left(x\sin x\right)=$$  #7

• $$\cos x$$  

• $$x\sin x+\cos x$$  

• $$x\cos x+\sin x$$  

• $$x\sin x-\cos x$$  

Multiple Choice

$$\frac{d}{dx}\left(\sin x+\cos x\right)=$$  #8

• $$\sin x+\cos x$$  

• $$\sin x-\cos x$$  

• $$-\sin x+\cos x$$  

• $$-\sin x-\cos x$$  

Multiple Choice

$$\frac{d}{dt}\left(4\sec t+\tan t\right)=$$  #9

• $$4\tan t+\sec t$$  

• $$4\sec t+\tan t$$  

• $$\tan t\left(4\sec t+\tan t\right)$$  

• $$\sec t\left(4\tan t+\sec t\right)$$  

Multiple Choice

$$\frac{d}{d\theta}\left(\theta\csc\theta-\cot\theta\right)=$$  #10

• $$\csc\theta\left(-\theta\cot\theta+1+\csc\theta\right)$$  

• $$\csc\theta\left(-\theta\csc\theta+1+\cot\theta\right)$$  

• $$\cot\theta\left(-\theta\cot\theta+1+\csc\theta\right)$$  

• $$\cot\theta\left(-\theta\csc\theta+1+\cot\theta\right)$$  

Multiple Choice

$$\frac{d}{dx}\left(\frac{\sin x}{1+\cos x}\right)=$$  #11

• $$\frac{\cos x}{-\sin x}$$  

• $$\frac{-\sin^2x-\cos x+\cos^2x}{\left(1+\cos x\right)^2}$$  

• $$\frac{1}{1+\cos x}$$  

• $$\frac{-\cos^2x+\cos x+\sin^2x}{\left(1+\cos x\right)^2}$$  

Multiple Choice

$$\frac{d}{dx}\left(\frac{\tan x-1}{\sec x}\right)=$$  #12

• $$\frac{\sec x}{\tan x}$$  

• $$\frac{\sec^2x-\tan^2x-\tan x}{\sec x}$$  

• $$\frac{\tan^2x+\tan x-\sec^2x}{\sec x}$$  

• $$\frac{1+\tan x}{\sec x}$$  

Multiple Choice

$$\frac{d}{dx}\left(\frac{\sin x}{x^2}\right)=$$  #13

• $$\frac{\cos x}{2x}$$  

• $$\frac{x\cos x-2\sin x}{x^3}$$  
  

• $$\frac{2\cos x-x\sin x}{x^3}$$  

• $$\frac{x^2\cos x+2\sin x}{x^4}$$  

Multiple Choice

$$\frac{d}{dx}\left[\sin\left(x^2+x\right)\right]$$  #14

• $$\left(2x+1\right)\cos\left(x^2+x\right)$$  

• $$\cos\left(2x+1\right)$$  

• $$\cos\left(x^2+x\right)$$  

Multiple Choice

$$\frac{d}{dx}\left[\cos\left(e^x\right)\right]$$  #15

• $$-\sin\left(e^x\right)$$  

• $$e^x$$  

• $$-e^x\sin\left(e^x\right)$$  

Multiple Choice

$$\frac{d}{dx}\left[\sin x\cos x\right]$$  #16

• 1

• $$-\sin x\cos x$$  

• $$\cos^2x-\sin^2x$$  

Multiple Choice

Find the derivative f(x) = tanxcosx #17

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx