Question

(log x)^{x} + x^{log x} प्रदत्त फलनों का x के सापेक्ष अवकलन कीजिए

Answer 1

$dy/dx = (logx)^{x} ( log(log(x)) + 1/log(x)) + x^{log x} \times 2log(x) /x$

Step-by-step explanation:

$y = (log x)^{x} + x^{log x}$

y = u  + v

dy/dx = du/dx  + dv/dx

u  = (logx)ˣ

log u  = x log(log(x))

=> 1/u  du/dx  = log(log(x))  + x  (1/log(x))(1/x)

=> du/dx = u  ( log(log(x) + 1/log(x))

=> du/dx = (logx)ˣ  ( log(log(x)) + 1/log(x))

$v = x^{log x}$

log v  = logx * log (x)

=> log v  = (log(x) )²

=> (1/v) dv/dx = 2log(x) /x

=> dv/dx = v *  2log(x) /x

$dv/dx = x^{log x} \times 2log(x) /x$

$dy/dx = (logx)^{x} ( log(log(x)) + 1/log(x)) + x^{log x} \times 2log(x) /x$

और अधिक जानें :

sin(x²+5)"

brainly.in/question/15286193

sin (ax+b) फलन का अवकलन कीजिए

brainly.in/question/15286166