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

1 Answer
Nov 8, 2015

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

Explanation:

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