Question

relative rate of change for f(x)= 5x - xlnx

Answer 1

Same deal as before. From the definition,\[\frac{f'(x)}{f(x)}=\frac{5-(\ln x+1)}{5x-x \ln x}=\frac{4-\ln x}{x(5-\ln x)}\]

Answer 2

Are you having trouble with taking the derivative?

Answer 3

yeah i wasnt sure how to get the derivative.

Answer 4

jsut when you have ln

Answer 5

I'm thinking it's the xlnx bit?

Answer 6

\[\frac{d}{dx}x \ln x=x \frac{d}{dx}\ln x+\ln x \frac{d}{dx}x=x \times \frac{1}{x}+\ln x \times 1\]\[=1+\ln x\]

Answer 7

So the entire derivative in the numerator is\[f'(x)=5-(1+\ln x)=4-\ln x\]

Answer 8

thanks

Answer 9

no worries

Answer 10

im trying to correct this test and this class is killing me

Answer 11

we'll do our best to help

Answer 12

Thanks

Answer 13

Thanks