Question

(cos x)^{y}= (cos y)^{x} प्रदत्त फलनों का x के सापेक्ष अवकलन कीजिए

Answer 1

$(dy/dx) = \frac{(Cosy)^x(log(cosy) + (cos x)^{y} ytanx}{ (cos x)^{y} log(cosx) + (Cosy)^x(xTany)}$

Step-by-step explanation:

dy/dx ज्ञात कीजिए

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

u = v

du/dx = dv/dx

$u = (cos x)^{y}$

log u  = y log (cosx)

(1/u) du/dx  = (dy/dx) log(cosx)  +  y (1/Cosx)(-Sin)

=> du/dx = u ( (dy/dx) log(cosx)  - ytanx)

=> $du/dx = (cos x)^{y} \times ( (dy/dx) log(cosx) - ytanx)$

v = (Cosy)ˣ

logv = x log(Cosy)

(1/v)dv/dx  = log(cosy)  +  x(1/Cosy)(-Siny)dy/dx

=> dv/dx = v (  log(cosy)  -  (xTany)dy/dx)

=>  dv/dx = (Cosy)ˣ (  log(cosy)  -  (xTany)dy/dx)

$(cos x)^{y} \times ( (dy/dx) log(cosx) - ytanx) = (Cosy)^x( log(cosy) - (xTany)dy/dx)$

$(dy/dx) = \frac{(Cosy)^x(log(cosy) + (cos x)^{y} ytanx}{ (cos x)^{y} log(cosx) + (Cosy)^x(xTany)}$

और अधिक जानें :

sin(x²+5)"

brainly.in/question/15286193

sin (ax+b) फलन का अवकलन कीजिए

brainly.in/question/15286166