let y = xn + nx + xx + nn
⇒ y = a + b + c + m
where a= xn; b = nx ; c = xx ; m= nn
\(\Bigg\{\) Using chain rule, \(\cfrac{d(u +a)}{d\text x}=\cfrac{du}{d\text x}+\cfrac{da}{d\text x}\) where a and u are any variables \(\Bigg\}\)
a = xn
Taking log both the sides:
⇒ log a= log xn
⇒ log a= n log x
{log xa = a log x}
⇒ log a= n log x {log e -1}
Differentiating with respect to x:
\(\Bigg\{\) Using chain rule, \(\cfrac{d(au)}{d\text x}\) = a\(\cfrac{du}{d\text x}\) where a is any constant and u is any variable\(\Bigg\}\)
b = nx
Taking log both the sides:
⇒ log b= log nx
⇒ log b= x log n
{log xa = a log x}
Differentiating with respect to x:
\(\Bigg\{\) Using chain rule, \(\cfrac{d(au)}{d\text x}\) = a\(\cfrac{du}{d\text x}\) where a is any constant and u is any variable\(\Bigg\}\)
c = xx
Taking log both the sides:
⇒ log c= log xx
⇒ log c= x log x
{log xa = a log x}
Differentiating with respect to x: