Trigo Differentiation Basics

Trigo Differentiation Basics

by Thavarajah Selvarajah

​RULE 1

​RULE 2

​

​LEVEL 1

​

​

DIFFERENTIATION USING RULE 1 AND RULE 2

​

​

Multiple Choice

Given $$y=\tan x$$  , $$\frac{\text{d}y}{\text{d}x}=?$$  

• $$\sec^2x$$  

• $$\sin^2x$$  

• $$\sec^2w$$  

• 1

Multiple Choice

$$\frac{\text{d}}{\text{d}w}\left(\tan w\right)=?$$  

• $$\sin^2w$$  

• $$\sec^2x$$  

• $$\sec^2w$$  

• 1

Multiple Choice

Given  $$y=-\operatorname{cosec}x$$  . Find  $$\frac{dy}{dx}$$  

• $$\operatorname{cosec}x\ \cot\ x$$  

• $$-\operatorname{cosec}x\cot x$$  

• $$\sec^2w$$  

• $$-\frac{1}{\sin x}$$  

Multiple Choice

Given  $$y=-\frac{3}{4}\operatorname{cosec}x$$  . Find  $$\frac{dy}{dx}$$  

• $$-\operatorname{cosec}x\ \cot x$$  

• $$\operatorname{cosec}x\cot x$$  

• $$\frac{3}{4}\operatorname{cosec}x\cot x$$  

• $$-\frac{3}{4}\operatorname{cosec}x\cot x$$

Multiple Choice

Given $$y=\frac{4}{5}\cot x$$  . What is $$\frac{dy}{dx}?$$  

• $$-\frac{4}{5}\operatorname{cosec}^2x$$  

• $$\frac{4}{5}\operatorname{cosec}^2x$$  

• $$\operatorname{cosec}^2x$$  

• $$-\operatorname{cosec}^2x$$  

Multiple Choice

Given $$y=-\frac{4}{5}\cot x$$  . What is $$\frac{dy}{dx}?$$  

• $$-\frac{4}{5}\operatorname{cosec}^2x$$  

• $$\frac{4}{5}\operatorname{cosec}^2x$$  

• $$\operatorname{cosec}^2x$$  

• $$-\operatorname{cosec}^2x$$  

Multiple Choice

$$y=\cos x-\sin x,\ \frac{\text{d}y}{\text{d}x}=?$$  

• $$\sin x-\cos x$$

• $$-\sin x-\cos x$$  

• $$\sec^2w$$  

• $$\sin x+\cos x$$

Multiple Choice

Given  $$y=-\sin x+\cos x$$  . What is  $$\frac{dy}{dx}=?$$  

• $$-\cos x-\sin x$$  

• $$\cos x-\sin x$$

• $$-\cos x+\sin x$$

• $$\cos x+\sin x$$

Multiple Choice

Given  $$y=-\sin x-\cos x$$  . What is  $$\frac{dy}{dx}=?$$  

• $$-\cos x-\sin x$$  

• $$\cos x-\sin x$$

• $$-\cos x+\sin x$$

• $$\cos x+\sin x$$

Multiple Choice

$$y=2\sin x-3\cot x$$  

           $$\frac{\text{d}}{\text{d}x}\left(y\right)=\frac{\text{d}}{\text{d}x}\left(2\sin x\right)-\frac{\text{d}}{\text{d}x}\left(3\cot x\right)$$  

$$p\ \ \ \ \ \ \ =\ \ \ q+r$$              

What is  $$p?$$  

• $$1$$  

• $$\frac{dy}{dx}$$  

• $$y$$  

• $$\frac{\text{d}x}{\text{d}y}$$  

Multiple Choice

$$y=2\sin x-3\cot x$$  

           $$\frac{\text{d}}{\text{d}x}\left(y\right)=\frac{\text{d}}{\text{d}x}\left(2\sin x\right)-\frac{\text{d}}{\text{d}x}\left(3\cot x\right)$$  

$$p\ \ \ \ \ \ \ =\ \ \ q+r$$                         

What is  $$q?$$  

• $$2\sin x$$  

• $$\cos x$$  

• $$-2\cos x$$  

• $$\text{2cos x}$$  

Multiple Choice

$$y=2\sin x-3\cot x$$  

           $$\frac{\text{d}}{\text{d}x}\left(y\right)=\frac{\text{d}}{\text{d}x}\left(2\sin x\right)-\frac{\text{d}}{\text{d}x}\left(3\cot x\right)$$  

$$p\ \ \ \ \ \ \ =\ \ \ q+r$$                         

What is  $$r?$$  

• $$-3\operatorname{cosec}^2x$$   

• $$3\operatorname{cosec}^2x$$  

• $$\operatorname{cosec}^2x$$  

• $$-\operatorname{cosec}^2x$$  

Multiple Choice

Given  $$y=-3\cos x-4\tan x$$  . What is  $$\frac{dy}{dx}=?$$  

• $$-3\sin x-4\sec^2x$$  

• $$3\sin x-4\sec^2x$$

• $$-\sin x-\sec^2x$$

• $$\sin x-\sec^2x$$

Multiple Choice

Given $$y=-\frac{5}{4}\cot x-3\sec x$$  . What is $$\frac{d}{dx}\left(-\frac{5}{4}\cot x-3\sec x\right)$$  

• $$-\frac{5}{4}\operatorname{cosec}^2x-3\sec x\tan x$$  

• $$\frac{5}{4}\operatorname{cosec}^2x-3\sec x\tan x$$

• $$-\frac{5}{4}\operatorname{cosec}^2x+3\sec x\tan x$$

• $$\frac{5}{4}\operatorname{cosec}^2x+3\sec x\tan x$$

​LEVEL 2

​Combining trigo with weapons of Differentiation

Multiple Choice

$$y=\cos x\sin x$$  .

What is the SUITABLE WEAPON we use to find $$\frac{\text{d}y}{\text{d}x}$$  

• Product rule

• Quotient rule

• Direct

• Chain Rule

Multiple Choice

$$y=\frac{1}{\sin x}$$  .

What is the SUITABLE WEAPON we use to find $$\frac{\text{d}y}{\text{d}x}$$  

• Product rule

• Quotient rule

• Power Rule

• Direct

Multiple Choice

$$y=\operatorname{cosec}x\sin x$$  .

What is the SUITABLE WEAPON we use to find $$\frac{\text{d}y}{\text{d}x}$$  

• Product rule

• Quotient rule

• Power Rule

• Direct

Multiple Choice

$$y=\frac{1}{\sin x}$$  .

What is the SUITABLE WEAPON we use to find $$\frac{\text{d}y}{\text{d}x}$$  

• Product rule

• Quotient rule

• Power Rule

• Direct

Multiple Choice

$$y=\sec x$$  .

What is the SUITABLE WEAPON we use to find $$\frac{\text{d}y}{\text{d}x}$$  

• Product rule

• Quotient rule

• Power Rule

• Direct

Multiple Choice

$$y=\frac{\cos\ x\ }{\sin x}$$  ,                      

$$\frac{\text{d}y}{\text{d}x}=\frac{\left(\sin x\right)p-\left(\cos x\right)q}{r}$$  .

What is  $$p?$$  

• $$-\cos x$$  

• $$\cos x$$  

• $$-\sin x$$  

• $$\sin x$$  

Multiple Choice

$$y=\frac{\cos\ x\ }{\sin x}$$  ,

$$\frac{\text{d}y}{\text{d}x}=\frac{\left(\sin x\right)p-\left(\cos x\right)q}{r}$$  .

What is  $$q?$$  

• $$-\cos x$$  

• $$\cos x$$  

• $$-\sin x$$  

• $$\sin x$$  

Multiple Choice

$$y=\frac{\cos\ x\ }{\sin x}$$  ,                      

$$\frac{\text{d}y}{\text{d}x}=\frac{\left(\sin x\right)p-\left(\cos x\right)q}{r}$$  .

What is  $$r?$$  

• $$\cos^2x$$  

• $$\cos x$$  

• $$\sin x$$  

• $$\sin^2x$$  

Multiple Choice

$$y=\frac{\sin\ x\ }{\cos x}$$  ,

$$\frac{\text{d}y}{\text{d}x}=\frac{\left(\cos x\right)p-\left(\sin x\right)q}{r}$$  .

What is  $$p?$$  

• $$-\cos x$$  

• $$\cos x$$  

• $$-\sin x$$  

• $$\sin x$$  

Multiple Choice

$$y=\frac{\sin\ x\ }{\cos x}$$  ,                       

$$\frac{\text{d}y}{\text{d}x}=\frac{\left(\cos x\right)p-\left(\sin x\right)q}{r}$$  .

What is  $$q?$$  

• $$-\cos x$$  

• $$\cos x$$  

• $$-\sin x$$  

• $$\sin x$$  

Multiple Choice

$$y=\frac{\sin\ x\ }{\cos x}$$  ,

$$\frac{\text{d}y}{\text{d}x}=\frac{\left(\cos x\right)p-\left(\sin x\right)q}{r}$$  .

What is  $$r?$$  

• $$\cos^2x$$  

• $$\cos x$$  

• $$\sin^2x$$  

• $$\sin x$$  

Multiple Choice

$$y=\left(\frac{1}{\cos x}\right)$$  

$$\frac{\text{d}}{\text{d}x}\left(y\right)=\left(\cos x\right)^{-1}$$  

$$p=r\left(\cos x\right)^q\left(s\right)$$  

What is $$r?$$  

• 1

• -1

Multiple Choice

$$y=\frac{1}{\cos x}$$  

$$\frac{\text{d}}{\text{d}x}\left(y\right)=\left(\cos x\right)^{-1}$$  

$$p=r\left(\cos x\right)^q\left(s\right)$$  

What is $$q?$$  

• 0

• -1

• -2

• 2

Multiple Choice

$$y=\frac{1}{\cos x}$$  

$$\frac{\text{d}}{\text{d}x}\left(y\right)=\left(\cos x\right)^{-1}$$  

$$p=r\left(\cos x\right)^q\left(s\right)$$  

What is $$s?$$  

• $$\cos x$$  

• $$\sin x$$  

• $$-\sin x$$  

• $$-\cos x$$  

Multiple Select

Given  $$y=\frac{1}{\cos x}$$  , find  $$\frac{\text{d}y}{\text{d}x}$$  

• $$\tan x\sec x$$  

• $$\frac{\sin x}{\cos^2x}$$  

• $$\sin x\sec^2x$$  

• $$\frac{1}{\cos^2x}$$  

Multiple Choice

Given  $$y=2\operatorname{cosec}x\sin x$$  , find  $$\frac{\text{d}y}{\text{d}x}$$  

• $$-2\operatorname{cosec}x\cot x$$  

• $$2$$  

• $$0$$  

• $$2\operatorname{cosec}x\cos x$$  

Multiple Choice

Given  $$y=\sin x\tan x$$  , find  $$\frac{\text{d}y}{\text{d}x}$$  

• $$\sin x+\sin x\sec^2x$$  

• $$-\sin x+\sin x\sec^2x$$  

• $$\cos x\sec^2x$$  

• $$\sin x+\sin x\sec^{ }x$$

Multiple Choice

Given  $$y=x\sin x\$$  , find  $$\frac{\text{d}y}{\text{d}x}$$  

• $$\cos x$$  

• $$x\cos x+\sin x$$  

• $$\sin x-x\cos x$$  

• $$x\sin x+\cos x$$  

Multiple Choice

Given  $$y=\frac{\cos x}{1-\sin x}$$  , find  $$\frac{\text{d}y}{\text{d}x}$$  

• $$\frac{1}{1-\sin x}$$  

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

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

• $$1-\sin x$$  

Multiple Choice

Given  $$y=2\cos x+3\operatorname{cosec}x$$  , find  $$\frac{\text{d}y}{\text{d}x}$$  

• $$2\sin x+3\operatorname{cosec}x\cot x$$   

• $$-2\sin x+3\cot x\operatorname{cosec}x$$  

• $$-2\sin x-3\operatorname{cosec}x\cot x$$

• $$-\sin x-\operatorname{cosec}x\cot x$$