Question

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

Answer 1

$dy/dx = x^{ sin x} (Cosx log(x) + Sinx/x) + (sin x)^{cos x} ( Cosx Cotx - Sinx log(Sinx))$

Step-by-step explanation:

dy/dx ज्ञात कीजिए

$y = x^{ sin x} + (sin x)^{cos x}$

$u = x^{ sin x}$   , $v = (sin x)^{cos x}$

y = u  +  v

dy/dx = du/dx  + dv/dx

$u = x^{ sin x}$

log u  = Sinx log(x)

(1/u ) du/dx   = Cosx log(x)  + Sinx/x

=>  du/dx   = u (Cosx log(x)  + Sinx/x)

=> $du/dx = x^{ sin x} (Cosx log(x) + Sinx/x)$

$v = (sin x)^{cos x}$

log v  = Cosx log(Sinx)

(1/v) dv/dx  =  -Sinx log(Sinx)  + Cosx * (1/Sinx) Cosx

=>  dv/dx  = v ( Cosx Cotx - Sinx log(Sinx))

=> $dv/dx = (sin x)^{cos x} ( Cosx Cotx - Sinx log(Sinx))$

और अधिक जानें :

sin(x²+5)"

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sin (ax+b) फलन का अवकलन कीजिए

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