If f(x)=log(1-x)/(1+x).then what will be the value of f'(0)?

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Answer 1 · 2018-01-30T18:08:40

# -2#.

I presume that #log# means natural log, i.e., #ln#.

#f(x)=log_e{(1-x)/(1+x)}=ln{(1-x)/(1+x)}#.

Using the usual rules of #log#, we have,

#f(x)=ln(1-x)-ln(1+x)#

#rArr f'(x)=d/dx{ln(1-x)}-d/dx{ln(1+x)}#,

#=1/(1-x)*d/dx(1-x)-1/(1+x)*d/dx(1+x)...............[because," the Chain Rule],"#

#=1/(1-x)*(-1)-1/(1+x)*1#,

#=1/(x-1)-1/(x+1)#,

#={(x+1)-(x-1)}/{(x+1)(x-1)}#,

#:. f'(x)=2/(x^2-1)#.

#rArr f'(0)=2/(0-1)=-2#.