Differentiate : y = x^2/x (PRAC TEST 2)

Question

Differentiate :

 

x^2/x

 

 

ANSWER: 2( 1 - ln(x)) * x^{2/x - 4/2}

#38, practice test

Answer 1

d/dx x^2/x

 

= d/dx exp(ln x^2/x)

 

= d/dx e^{(2 ln x)/x}

 

= 2e^{(ln x)/x} d/dx [(ln x)/x]

 

= 2x^2/x [(1/x)x - (ln x)1]/x²

 

= 2x^{2/x - 2} (1 - ln x)

 

This function is related to an interesting function f(x) = x^1/x for which I once conjectured that dⁿf/dxⁿ has exactly n positive real roots.