Differentiate f(x)= $x^(9x)$ ?

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Answer 1 · 2018-06-18T05:13:50

$color(blue)(f'(x) = 9x^(9x) [ln x + 1]$

$f(x) = x^(9x)$

$f'(x) = (d/(dx)) (x^(9x))$

$f'(x) = x^(9x) * (d / (dx)) (ln x * 9x)$

$f'(x) = 9 x^(9x) * [(ln x ) + (x * 1/x)]$

$color(blue)(f'(x) = 9x^(9x) [ln x + 1]$

Differentiate f(x)=x^(9x)x^(9x) ?