What is the derivative of #f(x)= log_3(3-2x)#?

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Answer 1 · 2016-01-09T19:53:48

#f'(x)=2/((2x-3)ln3)#

Use the change of base formula to express #f(x)# in terms of the natural logarithm.

#f(x)=ln(3-2x)/ln3#

Thus,

#f'(x)=1/ln3*d/dx(ln(3-2x))#

To find the derivative of a natural logarithm function, use the chain rule:

#d/dx(ln(u))=1/u*u'#

Thus,

#f'(x)=1/ln3*1/(3-2x)*d/dx(3-2x)#

#=1/ln3*1/(3-2x)*-2#

#=(-2)/((3-2x)ln3)#

#=2/((2x-3)ln3)#