Question

x^{y} + y^{x} = 1 प्रदत्त फलनों का x के सापेक्ष अवकलन कीजिए

Answer 1

(dy/dx) =  -  (yx^(y-1)  +  yˣ  logy)/(x^y logx   + xyˣ⁻¹ )

Step-by-step explanation:

dy/dx ज्ञात कीजिए

$x^{y} + y^{x} = 1$

u + v  = 1

=> du/dx  + dv/dx = 0

$u = x^{y}$

log u  = y logx

=> (1/u) du/dx  = logx (dy/dx)  + y/x

=> du/dx  = u  ( logx (dy/dx)  + y/x)

$du/dx = x^{y} ( logx (dy/dx) + \frac{y}{x})$

v = yˣ

log v = x log y

=> (1/v) dv/dx =  logy  + x (1/y) dy/dx

=> dv/dx = v ( logy  + (x/y)dy/dx)

=> dv/dx = yˣ ( logy  + (x/y)dy/dx)

(x^y)( logx (dy/dx)  + y/x) +  yˣ ( logy  + (x/y)dy/dx) = 0

=> (dy/dx) (x^y logx   + yˣ (x/y) )  = -  (x^y(y/x) +  yˣ  logy)

=>  (dy/dx) (x^y logx   + xyˣ⁻¹ )  = -  (yx^(y-1)  +  yˣ  logy)

=>  (dy/dx) =  -  (yx^(y-1)  +  yˣ  logy)/(x^y logx   + xyˣ⁻¹ )

और अधिक जानें :

sin(x²+5)"

brainly.in/question/15286193

sin (ax+b) फलन का अवकलन कीजिए

brainly.in/question/15286166