Derivative of logarithmic functions (check work)

[confused_07]

I am sure I murdered these, but from my understanding of the text, here's what I got:

a) f[x]= xlnx - x = lnx + ln(lnx) - x
f'[x]= (1/x) + [1/(1/x)]
= (1/x) + x

B) f[x]= x^5 lnx = [(5*lnx) + (lnx * 1)]
f'[x]= [5(1/x) + (1/x)]
= 6/x

c) f[x]= (lnx)^2 = ln(lnx) + ln(lnx)
f'[x]= [1/(1/x)] + [1/(1/x)]
= x + x = 2x

d) f[x]= (1-x)/(lnx) = ln(1-x) - ln(lnx)
f'[x]= -[1/(1/x)] - [1/(1/x)]
= -[1/(1-x)] - x

Please be gentle.......

 

[tkhunny]

I am very curious how your logarithms keep getting inside each other...

Note: Please strive for clear notation. I cannot tell what you mean by "=" in any of these descriptions. When does the function change to the derivative?

If f(x) = xln(x) - x

Then f'(x) = (x*(1/x) + ln(x)*1) - 1 = (1 + ln(x)) - 1 = ln(x)

Try B again.

 

[confused_07]

Reworked 'b" and made changes in post, reworking others now....

 

[tkhunny]

B) f[x]= x^5 lnx = [(5*lnx) + (lnx * 1)]
f'[x]= [5(1/x) + (1/x)]
= 6/x

I'm still very curious about your use of "=". It looks like your first usage is a transition to the derivative. Too bad you called it a derivative only on the next line. Make sure your notation means what you intend.

You have an x^5. The first derivative of that is 5*x^4. Your x^4 keeps disappearing.

If f(x) = x^5*ln(x)
Then f'(x) = x^5*(1/x) + ln(x)*(5*x^4)
Simplify.