Calculus + Natural Log + Derivative

Question

Let f(x)= -5ln(6x)

 

I can't figure out how to find the fourth derivative.

 

f'(x)= -5/x

 

f'(4)= ___

 

Answer 1

Write as a ploynomial:

f¹(x) = -5x^-1

f²(x) = 5x^-2

f³(x) = -10x^-3

f⁴(x) = 30x^-4

Answer 2

f(x) = -5 ln 6x = -5 (ln x + ln 6) = -5 ln x - 5 ln 6

 

f'(x) = -5/x = -5x^-1

 

f''(x) = 5x^-2

 

f'''(x) = -10x^-3

 

f⁽⁴⁾(x) = 30x^-4 = 30/x⁴

 

Also

 

f'(4) = -5/4