SES-FAD (Basic Algebra before Differentiation)

SES-FAD (Basic Algebra before Differentiation)

by Thavarajah Selvarajah

Multiple Choice

Is this ready for to find  $$\frac{\text{d}y}{\text{d}x}?$$  

$$y=\sqrt[3]{x}$$  

• Yes

• No

• Maybe

• Not sure

Multiple Choice

Is this ready for to find  $$\frac{\text{d}y}{\text{d}x}?$$  

$$y=\sqrt[3]{x}$$  

• Yes

• No

• Maybe

• Not sure

Multiple Choice

In order to find  $$\frac{\text{d}y}{\text{d}x},$$   $$y=\sqrt[]{x}$$  can be written as 

• $$y=x^{\frac{1}{2}}$$  

• $$y=x^2$$  

• Stay as  $$y=\sqrt[]{x}$$

Multiple Choice

In order to find  $$\frac{\text{d}y}{\text{d}x},$$   $$y=\sqrt[3]{x}$$  can be written as 

• $$y=x^{\frac{1}{3}}$$  

• $$y=x^3$$  

• Stay as  $$y=\sqrt[3]{x}$$

Multiple Choice

Is this ready for to find  $$\frac{\text{d}y}{\text{d}x}?$$  

$$y=x^{\frac{1}{4}}$$  

• Yes

• No

• Not Sure

• Maybe

Multiple Choice

Can SES-FAD be applied on this? $$y=x^2\left(2x+1\right)$$  

• Yes

• No

Multiple Choice

Choose the correct expansion for $$y=x^2\left(2x+1\right)$$  

• $$y=2x^2+x^2$$  

• $$y=3x^3$$  

• $$y=2x^3+x^2$$  

• $$y=2x^3$$  

Multiple Choice

Can SES-FAD be applied for  $$y=x\left(1+2x\right)^2$$  

• Yes

• No

• Not Sure

• Doesnt matter

Multiple Choice

Can SES-FAD be applied for  $$y=\sqrt[]{x}\left(\sqrt[]{x}+1\right)$$  

• Yes

• No

• Not Sure

• Doesnt matter

Multiple Choice

Can SES-FAD be applied for  $$y=x^3\left(2x+1\right)$$  

• Yes

• No

• Not Sure

• Doesnt matter

Multiple Choice

Given  $$y=\sqrt[]{x}\left(\sqrt[]{x}+1\right)$$  . Choose the CORRECT expansion upon applying                     SES-FAD.

• $$y=x+x^{\frac{1}{2}}$$  

• $$y=x+x^2$$

• $$y=x^4+x^2$$  

• $$y=x^{\frac{1}{4}}+x^{\frac{1}{2}}$$  

Multiple Choice

Choose the BEST simplification to aid differentation

$$y=\frac{2x+1}{x}$$  

• $$y=\frac{2x}{x}+\frac{1}{x}$$  

• $$y=\left(2x+1\right)x^{-1}$$  

• $$y=\frac{1}{x}\left(2x+1\right)$$  

• cancel $$x$$  at $$2x$$  and $$x$$  

Multiple Choice

Can SES-FAD be applied on  $$y=\frac{x^2}{x^2+1}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Can SES-FAD be applied on  $$y=\frac{2x}{1-2x}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Can SES-FAD be applied on  $$y=\frac{1+x^2}{x^2}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Choose the BEST simplification to aid the differentiation of $$y=\frac{1+x^2}{x^2}$$  

• $$y=\frac{1}{x^2}\left(1+x^2\right)$$  

• $$y=\frac{1}{x^2}+\frac{x^2}{x^2}$$  

• Cancel the $$x^2$$  top and bottom

• $$y=x^2\left(1+x^2\right)$$  

Multiple Choice

Can SES-FAD be applied on $$y=\frac{1}{\left(2x-1\right)^3}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Can SES-FAD be applied on $$y=\frac{x-1}{\left(2x-1\right)^3}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Can SES-FAD be applied on $$y=\frac{1}{2x^3}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Can SES-FAD be applied on $$y=\frac{1}{2x^{ }}?$$  

• Yes

• No

• Maybe

• Not Sure

Multiple Choice

Choose the CORRECT simplification step for $$y=\frac{1}{2x^2}$$  to ensure READY for differentiation

• $$y=2x^2$$  

• $$y=2x^{-2}$$  

• $$y=\frac{1}{2}x^{-2}$$  

• $$y=\frac{1}{2}x^2$$  

Multiple Choice

Choose the CORRECT simplification step for $$y=\frac{1}{2x^{ }}$$  to ensure READY for differentiation

• $$y=2x^{ }$$  

• $$y=2x^{-1}$$  

• $$y=\frac{1}{2}x^{-1}$$  

• $$y=\frac{1}{2}x^{ }$$  

Multiple Choice

Choose the CORRECT simplification step for $$y=\frac{3}{\left(1-2x^{ }\right)^2}$$  to ensure READY for differentiation

• $$y=3\left(1-2x\right)^{-2}$$  

• $$y=3\left(1-2x\right)^2$$

• $$y=\left(1-2x\right)^2$$

• $$y=\left(1-2x\right)^{-2}$$