If f(x)=lnx/x then f'(1)?

Question

A. 0 
B. 1 
C. 1-e 
D. -1

Answer 1

f(x ) = lnx / x

Differentiating on both sides we get,

f^'(x ) = d/dx (lnx / x )

This is the form of d/dx (u / v ) which is (vu' - uv') / v².

f^'(x ) = [ (x ) d/dx(lnx ) - (lnx ) d/dx(x ) ] / x²

f^'(x ) = [ x (1/x) - lnx(1) ] / x²

f^'(x ) = [ 1 - lnx ] / x²

Therefore f^'(1) = (1 - ln(1)) / (1)²

                          = (1 - 0)/1                        [since ln(1) = 0]

                          = 1/1 = 1.

If f(x ) = inx / x then f'(1) = 1.

The answer is B.