derivative of 6/lnx

Question

Need worked out solution and answer.

Answer 1

You can also use the chain rule.  The result is the same.

 

d/dx (6/lnx) = 6 d/dx (lnx)^-1 = 6 [-(lnx)^-2] d/dx (lnx)

 

d/dx (lnx) = 1/x

 

d/dx (6/lnx) = -6 / (x ln²x)

 

Both quotient and chain rule work well in this problem.  But if instead of the constant 6 you had a function of x in the numerator, you would likely have to use the quotient rule.

Answer 2

The Quotient Rule states that D_x (u/v) = (v D_x u - u D_x v)/v²

 

In this problem u = 6 and v = ln x

 

The derivative is:

 

[ln x (0) - 6 (1/x)]/[ln x]²

 

= -6/[x * (ln x)²]

 

Note: the derivative of a constant term, such as 6, is zero. The derivative of ln x = 1/x.