Exponential :Exp and Num base

Exponential :Exp and Num base

by Thavarajah Selvarajah

​

Meanwhile exponential functions....

​Recap :)

​Recap :)

​

​LEVEL 1

Multiple Choice

Given  $$y=e^{4x}$$  , find  $$\frac{dy}{dx}=?$$  

• $$e^{4x}$$  

• $$4e^{4x}$$  

• $$4xe^{4x}$$  

• $$e^{4x-1}$$  

Multiple Choice

Given $$y=5e^{\sqrt[]{x}},\ \ \ \ \ \frac{dy}{dx}=?$$  

• $$5\sqrt[]{x}e^{\sqrt[]{x}}$$  

• $$\frac{5\sqrt[]{x}}{2}e^{\sqrt[]{x}}$$  

• $$\frac{5}{\sqrt[]{x}}e^{\sqrt[]{x}}$$  

• $$\frac{5}{2\sqrt[]{x}}e^{\sqrt[]{x}}$$  

Multiple Choice

Given  $$y=\frac{2}{e^{x^3}}$$  , find  $$\frac{dy}{dx}=?$$  

• $$2e^{-x^3}$$  

• $$-6x^2e^{-x^3}$$  

• $$-2x^3e^{-x^3-1}$$  

• $$\frac{2}{3e^{x^3}}$$  

Multiple Choice

Given $$y=6e^{\frac{2}{x}}$$  , find $$\frac{dy}{dx}$$  

• $$\frac{12}{x}e^{\frac{2}{x}-1}$$  

• $$-\frac{12}{x^2}e^{\frac{2}{x}}$$  

• $$\frac{12}{x^2}e^{\frac{2}{x}}$$  

• $$12e^{\frac{2}{x}}$$  

Multiple Select

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

• $$3^{2x}\ln9$$  

• $$3^{2x}\left(2\ln3\right)$$  

• $$3^{2x}\ln6$$  

• $$3^{2x}\ln3$$  

Multiple Choice

Given  $$y=5^{x^2},\frac{dy}{dx}=?$$  

• $$x^25^{x^2-1}$$  

• $$5^{x^2}\left(2x\ln5\right)$$  

• $$5^{x^2}\ln\left(10x\right)$$  

• $$5^{x^2}\ln5$$  

Multiple Choice

Given $$y=4^{\frac{1}{x}},\frac{dy}{dx}=?$$  

• $$4^{\frac{1}{x}}\ln4$$  

• $$\frac{1}{x}4^{\frac{1}{x}-1}$$  

• $$\frac{-4^{\frac{1}{x}}}{x^2}\ln4$$  

• $$4^{\frac{1}{x}}\ln4\left(\frac{1}{x}\right)$$

​LEVEL 2: EXP DIF with other weapons

How did you fare in Level 1?

​OR

Multiple Choice

Given  $$y=\frac{2x}{e^{2x}}$$  , what is the BEST WEAPON to find  $$\frac{dy}{dx}?$$  

• Power Rule

• Direct

• Quotient Rule

• Product Rule

Multiple Choice

Given  $$y=\left(1-3x\right)e^{3x}$$  , what is the BEST WEAPON to find  $$\frac{dy}{dx}?$$  

• Power Rule

• Direct

• Quotient Rule

• Product Rule

Multiple Choice

Given  $$y=\left(1-3x\right)e^{3x}$$  ,  $$\frac{dy}{dx}=?$$  

• $$9xe^{3x}$$  

• $$-6e^{3x}+9xe^{3x}$$  

• $$-9xe^{3x}$$  

• $$-2e^{3x}-3xe^{3x}$$  

Multiple Choice

Given  $$y=\frac{1-2x}{e^{2x}}$$  , what is the BEST-WEAPON to find  $$\frac{dy}{dx}?$$  

• Direct

• Product Rule

• Quotient Rule

• Power Rule

Multiple Choice

Given $$y=\frac{1-2x}{e^{2x}}$$  , $$\frac{dy}{dx}=?$$  

• $$\frac{-4+4x}{e^{2x}}$$  

• $$\frac{-3+2x}{e^{2x}}$$  

• $$\frac{-4x}{e^{2x}}$$  

• $$-4e^{2x}+4xe^{2x}$$  

Multiple Choice

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

• $$4^{x^2-2x\ }\ln4$$  

• $$\left(2x\ln4\right)4^{x^2-2x}$$  

• $$\left(2x\ln4-2\ln4\right)4^{x^2-2x}$$

• $$\left(2x\ln4\right)4^{x^2-2x}$$

Multiple Choice

Given $$y=\sqrt[3]{1-e^{2x}}$$  , what is the BEST-WEAPON to find $$\frac{dy}{dx}=?$$  

• Direct

• Product Rule

• Quotient Rule

• Power Rule

Multiple Choice

Given $$y=\sqrt[3]{1-e^{2x}}$$  , $$\frac{dy}{dx}=?$$  

• $$\frac{1}{3}e^{2x}\left(1-e\right)^{-\frac{2}{3}}$$  

• $$-\frac{2}{3}e^{2x}\left(1-e^{2x}\right)^{-\frac{2}{3}}$$  

• $$\frac{2}{3}e^{2x}\left(1-e^{2x}\right)^{-\frac{2}{3}}$$

• $$-6e^{2x}\left(1-e^{2x}\right)^2$$

​What you are expected to have unlocked?

• ​Ability to differentiate exponential terms (LEVEL 1)

• ​Ability to carry out differentiation of exponential terms with some weapons ( LEVEL 2)