Question

Y= e raise to x raise to x....find derivatives

Answer 1

Answer:

$y = e^{x^{x} }$

Step-by-step explanation:

$y = e^{x^{x}}$

y = e raise x raise x

Taking log both sides

log y = x raise x log e

Taking log both sides

log log y = x log x log e

Differentiating both sides with respect to x

1 / log y × 1/y × dy /dx = ( x × 1/x + log x ) log e

1 / log y × 1/y × dy /dx = ( 1 + log x ) log e

1 / log y × 1/y × dy /dx = ( 1 + log x ) + log e × 1/x

dy / dx =  ( 1 + log x ) + log e/x  ×  y log y / 1