Question #8e13d

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Answer 1 · 2016-10-03T13:59:42

#= 4/(4x-5) #

If you're uncomfortable with this, set it up for the chain rule:

so re-write as #f(x)=ln (4x-5) = ln u(x)#

where # u(x) = 4x-5#

so #(df)/dx = (df)/(du) * (du)/dx#

#= 1/u * 4#

#= 4/(4x-5)#

Or if you're more fluent:

#d/dx ln (4x-5) #

#= 1/(4x-5) d/dx (4x-5) #

#= 1/(4x-5) * 4#

#= 4/(4x-5) #

Or in general terms

#d/dx ln (f(x)) #

#= ( f'(x))/(f(x)) #

#= 4/(4x-5)#