How do you differentiate #f(x)=x^3ln(x)-ln(x^4)#?

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Answer 1 · 2015-11-08T03:25:33

#x^2 + 3x^2ln(x) -4/x#

You can differentiate the two terms separately, so I'll go through one at a time.

#d/dx[x^3ln(x)]# Use Product rule

#x^3(ln(x))' + ln(x)(x^3)'#

#x^3(1/x) + ln(x)(3x^2)#

#x^2 + 3x^2ln(x)#

Now the other term
#d/dx[-ln(x^4)]#

#d/dx[-4ln(x)]# log properties let us move the #4# out.

#-4(1/x) = -4/x#

putting it all together...

#x^2 + 3x^2ln(x) -4/x#

you could also write it as

#x^2(1+ 3ln(x)) -4/x#

or

#(x^3+3 x^3 log(x)-4)/x#