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Differentiate logarithms

Authored by HALIMATUL BM

Mathematics

University

Used 29+ times

Differentiate logarithms
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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=ln2xy=\ln2x  

 dydx=12x\frac{dy}{dx}=\frac{1}{2x}  

 dydx=1x\frac{dy}{dx}=\frac{1}{x}  

 dydx=2x\frac{dy}{dx}=\frac{2}{x}  

 dydx=1x2\frac{dy}{dx}=\frac{1}{x^2}  

2.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=2ln(x2+3x)y=2\ln\left(x^2+3x\right)  

 dydx=2xx2+3x\frac{dy}{dx}=\frac{2x}{x^2+3x}  

 dydx=2x2+3x\frac{dy}{dx}=\frac{2}{x^2+3x}  

 dydx=2x+3x2+3x\frac{dy}{dx}=\frac{2x+3}{x^2+3x}  

 dydx=4x+6x2+3x\frac{dy}{dx}=\frac{4x+6}{x^2+3x}  

3.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=ln(x2x+1)y=\ln\left(\frac{x}{2x+1}\right)  

 dydx=1x22x+1\frac{dy}{dx}=\frac{1}{x}-\frac{2}{2x+1}  

 dydx=1x12x+1\frac{dy}{dx}=\frac{1}{x}-\frac{1}{2x+1}  

 dydx=1x+22x+1\frac{dy}{dx}=\frac{1}{x}+\frac{2}{2x+1}  

 dydx=1x+12x+1\frac{dy}{dx}=\frac{1}{x}+\frac{1}{2x+1}  

4.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=ln(xex)y=\ln\left(xe^x\right)  

 dydx=1x+ex\frac{dy}{dx}=\frac{1}{x}+e^x  

 dydx=1x+1\frac{dy}{dx}=\frac{1}{x}+1  

 dydx=1xex\frac{dy}{dx}=\frac{1}{xe^x}  

 dydx=1x1\frac{dy}{dx}=\frac{1}{x}-1  

5.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=ln(x2ex2)y=\ln\left(x^2e^{x^2}\right)  

 dydx=12x+ex2\frac{dy}{dx}=\frac{1}{2x}+e^{x^2}  

 dydx=12x+2x\frac{dy}{dx}=\frac{1}{2x}+2x  

 dydx=2x+2x\frac{dy}{dx}=\frac{2}{x}+2x  

 dydx=1x2+2x\frac{dy}{dx}=\frac{1}{x^2}+2x  

6.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=ln(x2+3)5y=\ln\left(x^2+3\right)^5 

 dydx=10xx2+3\frac{dy}{dx}=\frac{10x}{x^2+3} 

 dydx=5xx2+3\frac{dy}{dx}=\frac{5x}{x^2+3} 

 dydx=2xx2+3\frac{dy}{dx}=\frac{2x}{x^2+3} 

 dydx=10x2+3\frac{dy}{dx}=\frac{10}{x^2+3} 

7.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of

 y=lnx6y=\ln x^6  

 dydx=16x\frac{dy}{dx}=\frac{1}{6x}  

 dydx=6x\frac{dy}{dx}=\frac{6}{x}  

 dydx=16x\frac{dy}{dx}=\frac{1}{6x}  

 dydx=1x6\frac{dy}{dx}=\frac{1}{x^6}  

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