Trigo4:Combination

Trigo4:Combination

by Thavarajah Selvarajah

​LEVEL 1

PIT-STOP 1+2+3

​What you are expected to unlock?

• ​Deciding which weapons to use for Differentiation

• ​Next, doing it!

Multiple Choice

Given  $$y=\sin x-2\cos2x$$  .To find  $$\frac{dy}{dx}$$  , suitable PIT-STOP to be used are

• Direct, Chain Rule

• Direct,Direct

• Chain Rule, Chain Rule

• Direct,Power Rule

Multiple Choice

Given  $$y=\sin x-2\cos2x$$  ,  $$\frac{dy}{dx}$$  =?

• $$\cos x+4\sin2x$$  

• $$\cos x-2\sin2x$$  

• $$\cos x+2\sin2x$$  

• $$\cos x-4\sin2x$$  

Multiple Choice

Given  $$y=\sin2x-\cos^22x$$  .To find  $$\frac{dy}{dx}$$  , suitable PIT-STOP to be used are

• Chain rule, Power rule

• Direct, Power rule

• Chain Rule, Chain Rule

• Direct, Direct

Multiple Choice

Given  $$y=\sin2x-\cos^22x$$  ,  $$\frac{dy}{dx}$$  =?

• $$2\cos2x-2\cos2x$$  

• $$\cos2x+2\cos2x\sin2x$$  

• $$2\cos2x+4\sin2x\cos2x$$  

• $$2\cos2x-4\cos2x\sin2x$$  

Multiple Choice

Given  $$y=\frac{3}{4}\sin x-\cos\left(\frac{3}{4}x\right)$$  ,to find  $$\frac{dy}{dx}$$  the suitable PIT-STOP is

• Direct, Chain Rule

• Direct, Power Rule

• Direct, Direct

• Chain Rule,Chain Rule

Multiple Choice

Given  $$y=\frac{3}{4}\sin x-\cos\left(\frac{3}{4}x\right)$$  ,  $$\frac{dy}{dx}$$  =?

• $$\frac{3}{4}\cos x-\frac{3}{4}\sin\ \frac{3}{4}x$$  

• $$\frac{3}{4}\cos x+\frac{3}{4}\sin\ \left(\frac{3}{4}x\right)$$  

• $$\frac{3}{4}\sin x-\sin\ \frac{3}{4}x$$  

• $$\frac{3}{4}\sin x+\sin\ \frac{3}{4}x$$  

Multiple Choice

Given  $$y=4\cot2x+3\sec^2x$$  .To find  $$\frac{dy}{dx}$$  , suitable PIT-STOP to be used are

• Direct, Chain Rule

• Direct,Power Rule

• Chain Rule, Chain Rule

• Chain Rule,Power Rule

Multiple Choice

Given  $$y=4\cot2x+3\sec^2x$$  ,  $$\frac{dy}{dx}$$  =?

• $$4\operatorname{cosec}^22x+6\sec x$$  

• $$-8\operatorname{cosec}^22x+6\sec x$$  

• $$4\operatorname{cosec}^22x+6\sec^2x\tan x$$  

• $$-8\operatorname{cosec}^22x+6\sec^2x\tan x$$  

Multiple Choice

Given  $$y=4\operatorname{cosec}^2x-4\tan2x$$  .To find  $$\frac{dy}{dx}$$  , suitable PIT-STOP to be used are

• Power Rule, Direct 

• Direct,Chain Rule

• Chain Rule, Chain Rule

• Power Rule,Chain Rule

Multiple Choice

Given  $$y=4\operatorname{cosec}^2x-4\tan2x$$  , $$\frac{dy}{dx}$$  =?

• $$8\operatorname{cosec}^2x\cot x-8\sec^22x$$

• $$-8\operatorname{cosec}^2x\cot x-8\sec^22x$$  

• $$8\operatorname{cosec}x-4\sec^22x$$  

• $$-8\operatorname{cosec}^2x\cot x-4\sec^22x$$  

Multiple Choice

Given  $$y=2\cot\left(1-2x\right)+\frac{3}{4}\sin x$$  .To find  $$\frac{dy}{dx}$$  , suitable PIT-STOP to be used are

• Chain Rule, Direct 

• Direct,Chain Rule

• Chain Rule, Chain Rule

• Power Rule,Chain Rule

Multiple Choice

Given  $$y=2\cot\left(1-2x\right)+\frac{3}{4}\sin x$$  ,find  $$\frac{dy}{dx}$$  .

• $$4\operatorname{cosec}^2\left(1-2x\right)+\frac{3}{4}\cos x$$   

• $$-4\operatorname{cosec}^2\left(1-2x\right)+\frac{3}{4}\cos x$$  

• $$-2\operatorname{cosec}^2\left(1-2x\right)+\frac{3}{4}\cos x$$

• $$2\operatorname{cosec}^2\left(1-2x\right)+\frac{3}{4}\cos x$$

​LEVEL 2:

COMBINATION OF PIT-STOP 1+2+3

with

other Rules

​Instruction...

​For each of the question,

you are required to find y' followed by y''

Multiple Choice

Find  $$y'$$  of  $$y=\sin\ \left(x^2+1\right)$$  

• $$\cos\left(x^2+1\right)$$  

• $$2x\cos\left(x^2+1\right)$$

Multiple Choice

Find  $$y^{''}$$   for  $$y=\sin\left(x^2+1\right)$$  

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

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

• $$2\cos\left(x^2+1\right)-4x^2\sin\left(x^2+1\right)$$  

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

Multiple Choice

Given  $$y=\sin x\cos3x$$  , find  $$y'$$  

• $$\cos3x\cos x+\sin3x\sin x$$  

• $$-3\sin3x\sin x+\cos3x\cos x$$  

• $$\cos x\cos3x-\sin x\sin3x$$  

• $$\cos3x\cos x+3\sin3x\sin x$$  

Multiple Choice

Given  $$y=\sin x\cos3x$$  , find  $$y''$$  

• $$-6\sin3x\cos x-10\cos3x\sin x$$  

• $$-4\sin x\cos3x-4\sin3x\cos x$$  

• $$-2\sin3x\cos x-2\cos3x\sin x$$  

• $$-8\cos3x\sin x$$  

Multiple Select

Find  $$y'$$  of  $$y=\left(\tan3x\right)^2$$   

• $$2\tan3x\sec^23x$$  

• $$6\tan3x\sec^23x$$  

• $$6\tan3x\left(\sec3x\right)^2$$  

• $$2\tan3x$$  

Multiple Choice

Find  $$y''$$  of  $$y=\left(\tan3x\right)^2$$   

• $$18\sec^43x+36\sec^23x\tan^23x$$  

• $$6\sec^43x+12\sec^23x\tan3x$$  

• $$18\sec^43x+12\tan3x\sec3x$$  

• $$18\sec^43x+12\sec^23x\tan^23x$$  

Multiple Choice

Find  $$y'$$  for  $$y=-\operatorname{cosec}2x$$  

• $$-2\operatorname{cosec}2x\cot2x$$  

• $$2\operatorname{cosec}2x\cot2x$$  

• $$-\operatorname{cosec}2x\cot2x$$  

• $$\operatorname{cosec}2x\cot2x$$  

Multiple Choice

Find $$y''$$  for $$y=-\operatorname{cosec}2x$$  

• $$-2\operatorname{cosec}2x\cot^22x-4\operatorname{cosec}^32x$$  

• $$-4\operatorname{cosec}2x\cot^22x-4\operatorname{cosec}^32x$$  

• $$-2\cot^22x\operatorname{cosec}2x-2\operatorname{cosec}^32x$$  

​Hope it went well! review the ones you had trouble. Remember lecturer is watching ur progress :)