Q3. (i) If y = x^y, prove that x

dy / dx

=

y² / 1 - y log x

(ii) If x = e^x/y, prove that x

dy / dx

=

x - y / x log x

(iii) If x^y= e^{x - y}, prove that

dy / dx

=

log x / (log xe)²

(iv) If x¹⁶y⁹ = (x² + y)¹⁷, prove that

dy / dx

=

2y / x

Solution