Letf(x)=x^x,x belongs to (0,∞) and letg(x) be inverse of f(x) ,then g’(x) must be

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Aditya Gupta · Answer

we know that f(g(x))= x diff both sides using chain rule f’(g(x))*g’(x)=1 or g’(x)= 1/f’(g(x)) now f’(x)= x^x(1+lnx)= f(x)*(1+lnx) so f’(g(x))= f(g(x))*(1+lng(x)), but f(g(x))= x so f’(g(x))= x(1+lng(x)) so that g’(x)= 1/f’(g(x))= 1/x(1+lng(x)) option c is correct. kindly approve please :)

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Letf(x)=x^x,x belongs to (0,∞) and letg(x) be inverse of f(x) ,then g’(x) must be

Letf(x)=x^x,x belongs to (0,∞) and letg(x) be inverse of f(x) ,then g’(x) must be

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